Chapter 1.

1.1 Problem Statement

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

Compute the derivative of (f º g).

f(u) = $a·u+1, g(x) = sin($b·x)

1.2 Step 1

Question Sequence

Question 1.1

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

(f º g)'(x) =(f(g(x))' = AJHs0aiOXXYYKYMi58NY5Q==(g(x))·GlwRU+QAspKTpwBOi8WbrQ==

Correct.
Incorrect.

Question 1.2

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

Correct.
Incorrect.

1.3 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($b·x).

Question Sequence

Question 1.3

f(u) = $a·u+1

f'(u) = nc1ItEz0kR4=

Correct.
Incorrect.

Question 1.4

Thus, for all u = g(x) = sin($b·x),

f'(g(x)) = f'(sin($b·x)) = nc1ItEz0kR4=.

Correct.
Incorrect.

Question 1.5

Next we calculate g'(x).

g(x) = sin($b·x)

g'(x) = iSba6t70dtA=·cos(iSba6t70dtA=·x)

Correct.
Incorrect.

1.4 Step 3

Question 1.6

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

f(u) = $a·u+1 and g(x) = sin($b·x)

with

f'(g(x)) = $a and g'(x) = $b·cos($b·x).

(f º g)'(x) = f'(g(x))g'(x) = SFgqQUkJGdg=·cos(iSba6t70dtA=·x)

Correct.
Incorrect.