1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kakasveta [241]
3 years ago
6

For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th

e composite function. (The function is of the form f(x) = g(h(x)). Use non-identity functions for g(x) and h(x).) f(x) = 3(4x2 + 8)5
Mathematics
1 answer:
alexira [117]3 years ago
3 0

Answer:

The inner function is h(x)=4x^2 + 8 and the outer function is g(x)=3x^5.

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

Step-by-step explanation:

A composite function can be written as g(h(x)), where h and g are basic functions.

For the function f(x)=3(4x^2+8)^5.

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have 4x^2+8 inside parentheses. So h(x)=4x^2 + 8 is the inner function and the outer function is g(x)=3x^5.

The chain rule says:

\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)

It tells us how to differentiate composite functions.

The function f(x)=3(4x^2+8)^5 is the composition, g(h(x)), of

     outside function: g(x)=3x^5

     inside function: h(x)=4x^2 + 8

The derivative of this is computed as

\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

You might be interested in
Owen received $100 for his birthday.he wants to spend 2/10 of his money on a video game.he wants to spend 55/100 of his money on
babymother [125]
An easy way to solve fraction problems like this is to make each fraction have the same denominator.  Since he has $100, the denominator will be 100.
2/10=?/100    10*10=100  1*10=20   20/100 of his money he wants to spend on video games
55/100 already has 100 as its denominator, so he wants to spend 55/100 on a skateboard.
3/10=?/100   10*10=100   3*10=100  30/100 is how much he wants to spend on comic books.
Add all of the fractions together to see how much he wants to spend and if he has enough.
20/100+55/100+30/100=105/100
He wants to spend $105, which is $5 more than he has.
8 0
3 years ago
Please please help me!!
ElenaW [278]
Hey you can go on Gauthmath it will have more people online to help you
8 0
2 years ago
What is it multiplying by?<br><br><br>784.5, 78.45, 7.845,0.7845, 0.07845
katrin [286]

Answer:

10,100,1000,-10,-100,-1000

Step-by-step explanation:

3 0
3 years ago
Rotate the following point (- 5, 7) with a 90 degree CCW rotation
Sergio039 [100]

Given:

The point is (-5,7).

To find:

The image of the given point after 90 degrees counter clockwise rotation.

Solution:

If a point rotated 90 degrees counter clockwise, then

(x,y)\to (-y,x)

Let the given point is P(-5,7). Using the above rule, we get

P(-5,7)\to P'(-7,-5)

Therefore, the image of the given point after 90 degrees counter clockwise rotation is (-7,-5).

5 0
3 years ago
The sum of the digits in a two digit number is 5. If 27 is subtracted from the number then places of the digits are interchanged
EleoNora [17]

Please find the attached photograph for your answer

8 0
3 years ago
Other questions:
  • On Earth you weigh 54.5 kilograms, while on the moon you weigh 9,071 grams. How many more grams do you weigh on Earth than on th
    12·2 answers
  • Why are parabolsas used for
    15·2 answers
  • Rational roots of f(x)=5x^2-3x+3
    7·1 answer
  • The area of a square garden is 36 square feet. What is the side length of the garden
    11·2 answers
  • Convert standard form 4x-2y=6
    7·1 answer
  • Colin invests £1100 into his bank account. He receives 5% per year simple interest. How much will Colin have after 6 years?
    9·1 answer
  • A garden measuring 8 feet by 12 feet will have a walkway around it. The walkway has
    5·1 answer
  • Hii!! Please help me out. To help me understand the answer just say exactly which part I'm putting the number in and stuff.
    13·1 answer
  • Find the slope \mathrm{m}m of the line in the graph below. ​ ​ \mathrm{m} =m=
    14·1 answer
  • when the perimeter of a regular polygon is divided by 5 the lenght of a side is 25 cm what is the perimeter​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!