Find the derivative of y.
-$$y = \ln ( \sinh 6 x )$$
A) $\frac { 1 } { \sinh 6 x }$
B) $6 \operatorname { csch } 6 x$
C) $\operatorname { coth } 6 x$
D) $6 \operatorname { coth } 6 x$

Question

Quizplus · Accepted Answer

The derivative of $y = \ln(\sinh 6x)$ is found using the chain rule. The derivative of $\ln(u)$ is $\frac{1}{u}$, and the derivative of $\sinh(6x)$ is $6\cosh(6x)$. Thus, the derivative is $\frac{6\cosh(6x)}{\sinh(6x)} = 6\coth(6x)$.

Find the Derivative of Y y=ln⁡(sinh⁡6x)y = \ln ( \sinh 6 x )y=ln(sinh6x)

Find the Derivative of Y $y = \ln ( \sinh 6 x )$