Find the derivative of the following function. $p = 5 q e ^ { q ^ { 4 } }$
A) $p ^ { \prime } = 5 e ^ { q ^ { 4 } } \left( 4 q ^ { 4 } + 1 \right)$
B) $p ^ { \prime } = 5 e ^ { q ^ { 4 } } \left( 4 q ^ { 3 } + 1 \right)$
C) $p ^ { \prime } = 5 e ^ { q ^ { 4 } } \left( q ^ { 4 } + 5 \right)$
D) $p ^ { \prime } = 5 e ^ { q ^ { 4 } } \left( 4 q ^ { 4 } + 5 \right)$
E) $p ^ { \prime } = 5 e ^ { q ^ { 4 } } \left( 4 q ^ { 3 } + 5 \right)$

Question

Quizplus · Accepted Answer

To find the derivative of $p = 5q e^{q^4}$, we use the product rule and the chain rule. The derivative of $q$ is $1$, and the derivative of $e^{q^4}$ is $e^{q^4} \cdot 4q^3$ (using the chain rule). Applying the product rule, we get $p' = 5(e^{q^4} + q \cdot e^{q^4} \cdot 4q^3) = 5e^{q^4}(1 + 4q^4)$.

Find the Derivative of the Following Function p=5qeq4p = 5 q e ^ { q ^ { 4 } }p=5qeq4

Find the Derivative of the Following Function $p = 5 q e ^ { q ^ { 4 } }$