derivative of (a^x/Log a)?​

Answers

Answer 1
[tex]\large\bold{\underline{\underline{To \: \: Differentive:-}}}[/tex]

[tex]\sf{\dfrac{a^x}{log(a)} }[/tex]

(OR)

[tex]\sf{\dfrac{a^x}{ln(a)} }[/tex]

[tex]\large\bold{\underline{\underline{Solution:-}}}[/tex]

[tex]\sf{Let\ y=\dfrac{a^x}{ln(a)} }[/tex]

[tex]\sf{=\dfrac{d}{dx}\bigg[\dfrac{a^x}{ln(a)} \bigg] }[/tex]

(Linear differentiation)

[tex]\sf{=\dfrac{1}{ln(a)}.\dfrac{d}{dx}(a^x) }[/tex]

[tex]\sf{=\dfrac{ln(a)a^x}{ln(a)} }[/tex]

[tex]\boxed{\sf{=a^x}}[/tex]

[tex]\large\bold{\underline{\underline{Applied:-}}}[/tex]

✭ Linear differentiation

→ [tex]\sf{[a.b(x)+c.d(x)]'=a.b'(x)+c.d'(x)}[/tex]

✭ Exponential function rule

→ [tex]\sf{(a^x)'=ln(a).a^x}[/tex]

Answer 2

Answer:

a^x.

Step-by-step explanation:

y = a^x / log a

Assuming the log is to the base e:

y = (1/ log a) * a^x

Derivative of a^x:

Let u = a^x

log u = log a^x

log u = x log a

1/u * du/dx = log a

du/dx =  = u * log a

y = (1 / log a) * u

so  dy/du = 1/log a

and dy/dx = dy/du * du/dx

=  (1/log a )* log a u

= u

= a^x.


Related Questions

6. Which of the following lines is perpendicular to the line **
4y = -- 24 and passes through the point (6 - 2)
(A) y a 4x 22
(B) yax - 22
(C) y = 22
(D) y - 4x-22
(E) = 4x+18

Answers

B because you just work it out

Answer:b

Step-by-step explanation:

Its correct

What is the largest possible integral value in the domain of the real-valued function

f(x)=[tex]\frac{1}{\sqrt{800-2x} }[/tex]

Answers

Answer:

Max Value: x = 400

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

AntiderivativesIntegral Property: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Integration Method: U-Substitution[Integration] Reverse Power Rule: [tex]\int {x^n} \, dx = \frac{x^{n+1}}{n+1} + C[/tex]

Step-by-step explanation:

Step 1: Define

[tex]f(x) = \frac{1}{\sqrt{800-2x} }[/tex]

Step 2: Identify Variables

Using U-Substitution, we set variables in order to integrate.

[tex]u = 800-2x\\du = -2dx[/tex]

Step 3: Integrate

Define:                                                                                                            [tex]\int {f(x)} \, dx[/tex]Substitute:                                                                                         [tex]\int {\frac{1}{\sqrt{800-2x} } } \, dx[/tex][Integral] Int Property:                                                                                     [tex]-\frac{1}{2} \int {\frac{-2}{\sqrt{800-2x} } } \, dx[/tex][Integral] U-Sub:                                                                                           [tex]-\frac{1}{2} \int {\frac{1}{\sqrt{u} } } \, du[/tex][Integral] Rewrite:                                                                                          [tex]-\frac{1}{2} \int {u^{-\frac{1}{2} }} \, du[/tex][Integral - Evaluate] Reverse Power Rule:                                                 [tex]-\frac{1}{2}(2\sqrt{u}) + C[/tex]Simplify:                                                                                                         [tex]-\sqrt{u} + C[/tex]Back-Substitute:                                                                                            [tex]-\sqrt{800-2x} + C[/tex]Factor:                                                                                                           [tex]-\sqrt{-2(x - 400)} + C[/tex]

Step 4: Identify Domain

We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.

Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.

Find the slope of the line. Enter your answer as
a number, fraction, or undefined. Reduce to
lowest terms where necessary.

Answers

Answer:-3/5

Step-by-step explanation:

Rise over run

A store starts the day with 36 packages of juice boxes.Each package contains the same number of juice boxes.By the end of the day,ther are only 8packages of juice boxes left.

Answers

Answer:

Number of package sold = 24 package

Step-by-step explanation:

Given:

Total number of package = 36

Remain package = 8

Computation:

Number of package sold = Total number of package - Remain package

Number of package sold = 36 - 8

Number of package sold = 24 package

Given the side lengths, determine whether the triangle is acute,right, obtuse, or not a triangle

Answers

Answer:

acute angle

Step-by-step explanation:

just took the test

And a survey of 500 households 23% say that they have a dog as a pet the standard deviation is 2% determine an interval that if I need to contain the 95% of all households who has a dog as a pet

Answers

Answer:

(114.123, 115.877)

Step-by-step explanation:

Given that :

Sample size (n) = 500

Mean = 23% of 500 = 115

Standard deviation (s) = 2% of 500 = 10

α = 95%

Zcritical at 95% = 1.96

Confidence interval = Mean ± Error

Error = Zcritical * standard deviation /sqrt (n)

Error = 1.96 * 10/sqrt(500)

Error = 0.8765386

Lower boundary : 115 - 0.8765386 = 114.1234614

Upper boundary : 115 + 0.8765386 = 115.8765386

(114.123, 115.877)

Question : If lines BG and CF are parallel, then OLF = OMG. Is this statement correct? Explain your answer.

Answers

Answer:

Yes this statement is correct.

Step-by-step explanation:

just mental math

The statement given that ∠OLF = ∠OMG is found to be; Correct from theorem of corresponding angles.

We are told that;

BC is parallel to CF

Now, we are told that;

∠OLF = ∠OMG

We can see that line DH is a transverse line that crosses the two parallel lines given as BG and CF

Now, according to theorem of corresponding angles, the angle's that are formed when two parallel lines are crossed by a transverse line are said to be equal because they correspond to one another.

In conclusion, it is true from corresponding angles that ∠OLF and ∠OMG are equal.

Read more about corresponding angles at; https://brainly.com/question/12054594

REALLY URGENT!!!!! ANSWER FAST!!!!

Answers

Answer:

if am sure it's A

Step-by-step explanation:

Geometry...Please help as soon as possible please and Thank you so much!

Answers

Answer:

Step-by-step explanation:

Statement1. ∠KJL ≅∠LMK (A)

Reason1. Given

Statement2. ∠JKL≅∠MLK (A)

Reason2. Given

Statment3. KL≅KL (S)

Reason3. Reflexive propriety

Statemnt 4. ΔJKL≡ΔLMK

Reason 4. AngleAngleSide congruency theorem

4 ten and 17 hundredth in decimals UNSERIOUS ANSWERS REPORTED

Answers

Answer:

40.17

Step-by-step explanation:

4 ten: 4 × 10 = 40

17 hundredth: 17 × 0.01 = 0.17

4 ten and 17 hundredth in decimals: 40 + 0.17 = 40.17

please solve will give brainiest

Answers

Step-by-step explanation:

BODMAS

155.5-5.5*20.7

155.5-113.85

=41.65

Answer:

41.65

Step-by-step explanation:

155.5-(5.5*20.7) order of operation

155.5-113.85=

41.65

n + 1 < −8
the solution of the inequality is ____?

Answers

Answer:

n < -9

Step-by-step explanation:

Subtract 1 from both sides: n < -8 -1

Simplify -8 -1 to -9

n < -9

Brainliest Please!!?!!!

- Hermionia

Which are the solutions of the inequality − 2x > − 4?
Choose all that apply.
A 2
B 1.5
C 1
D 3.5
E 2.5
F −2

ASAP!!!!!!!

Answers

Answer:

B,C&F

Step-by-step explanation:

-2x>-4

multiplied by -1 gives 2x<4

And you devide both sides by 2 you get x<2

The numbers smaller than 2 in your options are 1,1.5 and -2

what is

-5x-y=21
y=4x+6​

Answers

Answer:

(x,y)= (-3,-6)

Step-by-step explanation:

Answer:

Substitution substitution

Step-by-step explanation:

(-3,-6)

or

x= -3 y=-6

The measure of angle DCF is ... degrees?

Answers

Answer: Yes, The measure of DCF is degrees.

will mark brainliest, what are the missing numbers?

Answers

Answer:

117

Step-by-step explanation:

Got it from calucaltor and did it to make sure

Answer:

117

Step-by-step explanation:

help find this please

Answers

Answer:

B

Step-by-step explanation:

PLS I NEED THIS TO BE DONE IMMEDIATELY PLS PLS ;-;. which has the greater maximum value: f(x)=-3x^2+6x4, or g(x), the function in the graph

A. f(x)

B. the functions have the same maximum value.

C. g(x)

Answers

Answer:

A.f(x)

Step-by-step explanation:

Sup dude it's been a while since khelcee talked to us.

At the bookstore, Tim bought a magazine for $4, and five books that all cost the same amount. He spent a total of $129. Which equation expresses how much each book cost?

Answers

Answer:

25(b) + 4 = 129

Step-by-step explanation:

b=5

25(5) + 4=129

Lamar drinks 8 ounces of water with breakfast, 6 ounces of water with his vitamins, 16 ounces of water with his lunch, 16 ounces of water with his dinner, and 32 ounces of water from a bottle he carries throughout the day. Write and evaluate a numerical expression for the amount of water in ounces that he drinks in a week.

Answers

Given:

Lamar drinks water with,

Breakfast = 8 ounces

Vitamins = 6 ounces

Lunch = 16 ounces

Dinner = 16 ounces

Bottle = 32 ounces

To find:

The a numerical expression for the amount of water in ounces that he drinks in a week.

Solution:

One day consumption of water by Lamar is

[tex]8+6+16+16+32=78[/tex]

We know that,

1 week = 7 days

One day consumption of water = 78 ounces

1 week (7 days) consumption of water = 7× One day consumption of water

                                                               = 7×(8+6+16+16+32) ounces                                                                

                                                               = 7×78 ounces

                                                               = 546 ounces

Therefore, the required numerical expression for the amount of water in ounces that he drinks in a week is 7×(8+6+16+16+32) ounces and the value is 546 ounces.  

Naomi can make 20 tacos in 10 minutes. How many tacos can she make in 1 minute?

Answers

Answer:

2 tacos

Step-by-step explanation:

10 × 2 = 20

1 × 2 = 2

How do I find the measurement indicated in each parallelogram.

Answers

Answer:

17) 23

18) 12

Step-by-step explanation:

17

x+15 = 7+2x

x-2x = 7-15

-x= -8

x=8

WX = x+15

= 8+15

= 23

18

2x = 3x-6

2x -3x = -6

-x = -6

x = 6

EF = 3x-6

= 3(6) -6

= 18 -6

= 12

Answer is 17 u need to write 17

LOOK AT THE PICTURE

Please help I’m on a test will mark brainliest!

Answers

Answer:

2/7

Step-by-step explanation:

You have to flip the fraction to check, you see what times 3 gets you six... 2!

then what times one gets you 7.. 7! and that how you get 3/7

Kąty α i β są kątami przyległymi. Kąt wyznaczony przez dwusieczne kątów α oraz β ma miarę A) 90∘ B) 4 5∘ C) 60∘ D) różną, w zależności od miar kątów α i β

Answers

Answer:

i have

Step-by-step explanation:

i dont even know good luck

find the length of the side of a square with a perimeter of 128 meters​

Answers

Answer:

32 Meters

Step-by-step explanation:

A square has 4 equal sides so all you have to do is divide 128 by 4

........................divide

convert 3 4/5 into a improper fraction with steps please

Answers

Answer:

Step-by-step explanation:

((3×5)+4)/5=

19/5

The improper fraction is 19/5.

We have to convert [tex]3 \dfrac{4}{5}[/tex]  it into an improper fraction.

To convert into an improper fraction calculation must be done in a single unit following all the steps given below.

 Step1; Write the fraction into simple fractions,

                    [tex]= \dfrac{3 \times 5 + 4}{5}[/tex]

Step2; Solve the following equation.

                    [tex]=\dfrac{15+4}{5}\\\\=\dfrac{19}{5}[/tex]

Hence, The improper fraction is 19/5.

To know more about Fractions click the link given below.

https://brainly.com/question/21449807

(WORTH 20 POINTS) Please help I don't know how to do this

In your own words, what do the terms sales tax and discount mean? Is a 5 percent sales tax a percent of increase or decrease? What about a 15 percent discount?


lol help-

Answers

Answer:

Sales tax is an increase in the price of the item while a discount is the decrease of the price. A 5% sales tax is an increase since your paying an extra 5% of the item price. 15% discount is a decrease since your now only paying 85% of the original price. Hope that helps

Answer: In layman's terms, that means if the original price of something you sell was $100, but you offer a 50% discount, then the taxable price is $50. Sale Price = original price – (% of discount * original price)

Sales Tax = Sales Tax rate * Sale Price.

Sales Tax = 0.05 * $17.21 = $0.8605 = $0.86. How do I add 5% to a number?

Divide the number you wish to add 5% to by 100.

Multiply this new number by 5.

Add the product of the multiplication to your original number.

Enjoy working at 105%!

the bee hummingbird is the smallest bird. it can weigh as little as 2 grams. the largest bird, the ostrich, can weigh as much as 150 kilograms. the hummingbird's weight is what percent of the ostrich weight?

Answers

Answer:

1.3%

Step-by-step explanation:

i dont have an explanation

1.33 percent

When you divide 2 by 150 you get .0133333333. You move the decimal point two places to the right because it is a percentage out of 100. You round the number because the 3s continue forever.

Solve the inequality. 4v + 9 ≤ 5 or -3 >= -6​

Answers

Answer:

v ≤  − 1   or  Always true

Step-by-step explanation:

I hope this helps!

Answer:

v ≤  − 1

Step-by-step explanation:

PLZ HELP ME 30 POINTS TROLLERS WILL BE REPORTED

Answers

Answer:

56.25 B (haha troll go brrr)

Step-by-step explanation:

the ratio of the triangle measurements are:

60/45=75/x

60x=3375

x=56.25, therefore the distance of the new bridge is 56.25

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