Find the derivative of $h ( x ) = \left( 4 x ^ { 3 } + e ^ { x } \right) ^ { 3 }$ .
A) $3 \left( 4 x ^ { 3 } + e ^ { x } \right) ^ { 2 } \left( 12 x ^ { 2 } + e ^ { x } \right)$
B) $3 \left( 4 x ^ { 3 } + e ^ { x } \right) ^ { 2 } \left( 12 x ^ { 2 } + x e ^ { x - 1 } \right)$
C) $3 \left( 4 x ^ { 3 } + e ^ { x } \right) ^ { 2 }$
D) $3 \left( 12 x ^ { 2 } + e ^ { x } \right) ^ { 2 }$

Question

Quizplus · Accepted Answer

To find the derivative of $h(x) = (4x^3 + e^x)^3$, we use the chain rule. First, differentiate the outer function, which gives $3(4x^3 + e^x)^2$, and then multiply by the derivative of the inner function, $12x^2 + e^x$, resulting in $3(4x^3 + e^x)^2(12x^2 + e^x)$.

Find the Derivative Of h(x)=(4x3+ex)3h ( x ) = \left( 4 x ^ { 3 } + e ^ { x } \right) ^ { 3 }h(x)=(4x3+ex)3

Find the Derivative Of $h ( x ) = \left( 4 x ^ { 3 } + e ^ { x } \right) ^ { 3 }$