Find the derivative of y.
-$$y = \ln ( \sinh 5 x )$$
A) $\operatorname { coth } 5 x$
B) $5 \operatorname { csch } 5 x$
C) $5 \operatorname { coth } 5 x$
D) $\frac { 1 } { \sinh 5 x }$

Question

Quizplus · Accepted Answer

We can use the chain rule to find the derivative of y:
\begin{align*}
\frac{dy}{dx} &= \frac{1}{\sinh(5x)}\cdot \frac{d}{dx} \sinh(5x)\
&= \frac{1}{\sinh(5x)}\cdot 5\cosh(5x)\
&= 5\cdot\frac{\cosh(5x)}{\sinh(5x)}\
&= 5 \operatorname{coth}(5x)
\end{align*}
Therefore, the answer is C.

Find the Derivative of Y y=ln⁡(sinh⁡5x)y = \ln ( \sinh 5 x )y=ln(sinh5x)

Find the Derivative of Y $y = \ln ( \sinh 5 x )$