Let f(x) = $x ^ { 3 }$ . Using the chain rule, find an expression for the derivative of [f(g(x))].
A) 3 $x ^ { 2 }$ g'(x $) ^ { 3 }$
B) 3[g(x) $] ^ { 2 }$
C) g'(x $) ^ { 3 }$
D) 3[g(x) $] ^ { 2 }$ g'(x)
E) none of these

Question

Quizplus · Accepted Answer

The derivative of $f(g(x))$ using the chain rule is $f'(g(x)) \cdot g'(x)$. Given $f(x) = x^3$, $f'(x) = 3x^2$. Thus, the derivative of $f(g(x))$ is $3[g(x)]^2 \cdot g'(x)$.

Let F(x) = x3x ^ { 3 }x3 Using the Chain Rule, Find an Expression for the the Chain

Let F(x) = $x ^ { 3 }$ Using the Chain Rule, Find an Expression for the the Chain