Find the derivative of the function. $\frac { e ^ { - 5 x } } { 5 x e ^ { 5 x } }$
A) $- \frac { 10 x - 1 } { 5 x ^ { 2 } e ^ { 10 x } }$
B) $\frac { 10 x + 1 } { 5 x ^ { 2 } e ^ { 10 x } }$
C) $- \frac { 10 x + 1 } { x ^ { 2 } e ^ { 10 x } }$
D) $- \frac { 10 x + 1 } { 5 x ^ { 2 } e ^ { 10 x } }$
E) none of these

Question

Find the derivative of the function.   $\frac { e ^ { - 5 x } } { 5 x e ^ { 5 x } }$  
A)  $- \frac { 10 x - 1 } { 5 x ^ { 2 } e ^ { 10 x } }$
B)   $\frac { 10 x + 1 } { 5 x ^ { 2 } e ^ { 10 x } }$
C)   $- \frac { 10 x + 1 } { x ^ { 2 } e ^ { 10 x } }$
D)   $- \frac { 10 x + 1 } { 5 x ^ { 2 } e ^ { 10 x } }$
E) none of these

Quizplus · Accepted Answer

To find the derivative of the given function $\frac { e ^ { - 5 x } } { 5 x e ^ { 5 x } }$, we can simplify it first to $\frac { 1 } { 5 x e ^ { 10 x } }$. Using the quotient rule and the chain rule, the derivative is $- \frac { 10 x + 1 } { 5 x ^ { 2 } e ^ { 10 x } }$.

Find the Derivative of the Function e−5x5xe5x\frac { e ^ { - 5 x } } { 5 x e ^ { 5 x } }5xe5xe−5x​

Find the Derivative of the Function $\frac { e ^ { - 5 x } } { 5 x e ^ { 5 x } }$