Problem Statement

{3,5,7,9}
{2,4,6,8}
5*2

Compute the derivative of (f º g).

f(u) = 5·u+1, g(x) = sin(2·x)

 
Step 1

Question Sequence

Question 1

Recall the chain rule for differentiating (f º g)(x):

(f º g)'(x) =(f(g(x))' = (g(x))·

Correct.
Incorrect.

Question 2

For the given functions, observe that f is a function of u, and g is a function of .

Correct.
Incorrect.

 
Step 2

In order to substitute appropriately into the chain rule to compute,

(f º g)'(x) = (f(g(x)))' = f'(g(x))g'(x),

we need to find f'(g(x)), which is f'(u) evaluated at g(x) = sin(2·x).

Question Sequence

Question 3

f(u) = 5·u+1

f'(u) =

Correct.
Incorrect.

Question 4

Thus, for all u = g(x) = sin(2·x),

f'(g(x)) = f'(sin(2·x)) = .

Correct.
Incorrect.

Question 5

Next we calculate g'(x).

g(x) = sin(2·x)

g'(x) = ·cos(·x)

Correct.
Incorrect.

 
Step 3

Question 6

Applying the chain rule, find the derivative of (f º g) where

f(u) = 5·u+1 and g(x) = sin(2·x)

with

f'(g(x)) = 5 and g'(x) = 2·cos(2·x).

(f º g)'(x) = f'(g(x))g'(x) = ·cos(·x)

Correct.
Incorrect.