Find $\frac { d y } { d x }$ if $y = e ^ { 5 x ^ { 5 } }$ .
A) $\frac { d y } { d x } = 5 e ^ { 5 x }$
B) $\frac { d y } { d x } = e ^ { 5 x ^ { 5 } }$
C) $\frac { d y } { d x } = 5 x ^ { 5 } e ^ { 5 x ^ { 5 } - 1 }$
D) $\frac { d y } { d x } = 25 x ^ { 4 } \ln \left( 5 ^ { 5 } \right)$
E) $\frac { d y } { d x } = 25 x ^ { 4 } e ^ { 5 x ^ { 5 } }$

Question

Quizplus · Accepted Answer

To find $\frac{dy}{dx}$ for $y = e^{5x^5}$, we use the chain rule. The derivative of $e^{5x^5}$ with respect to $x$ is $e^{5x^5}$ times the derivative of the exponent $5x^5$, which is $25x^4$. Therefore, $\frac{dy}{dx} = 25x^4e^{5x^5}$.

Find dydx\frac { d y } { d x }dxdy​ If y=e5x5y = e ^ { 5 x ^ { 5 } }y=e5x5

Find $\frac { d y } { d x }$ If $y = e ^ { 5 x ^ { 5 } }$