Find and simplify the derivative of y = ln sech x.
A) tanh x
B) -tanh x
C) -sech x
D) -ln tanh x
E) sech x

Question

Quizplus · Accepted Answer

The derivative of $y = \ln(\text{sech } x)$ can be found using the chain rule. The derivative of $\ln(u)$ is $\frac{1}{u}\frac{du}{dx}$, and the derivative of $\text{sech } x$ is $-\text{sech } x \tanh x$. Therefore, the derivative of $y$ with respect to $x$ is $\frac{-\text{sech } x \tanh x}{\text{sech } x} = -\tanh x$.

Find and Simplify the Derivative of Y = Ln Sech