If f(x)= sin6 x and g(x) = e^(3+2x ) , how do you differentiate f(g(x)) using the chain rule?

1 Answer
Jan 6, 2016

Step by step explanation is given below.

Explanation:

Chain rule (f(g(x)))' = f'(g(x))**g'(x)

f(x) = sin(6x)
Differentiating with respect to x using chain rule

f'(x) = cos(6x)d/dx(6x)
f'(x) = 6cos(6x)

g(x) = e^(3+2x)
Differentiating with respect to x using chain rule
g'(x) = e^(3+2x)d/dx(3+2x)
g'(x)=e^(3+2x)(2)
g'(x)=2e^(3+2x)

We are to find derivative of f(g(x))

f'(g(x)) = 6cos(6e^(3+2x))

Using the chain rule
(f(g(x)))' = f'(g(x))**g'(x)

(f(g(x)))' = 6cos(6e^(3+2x))(2e^(3+2x))

(f(g(x)))' = 12e^(3+2x)cos(6e^(3+2x)) Answer