Question

Find the derivative of y with respect to z.y = ln (sinh 9z)

Answer 1

The given function is:

`y=\ln (\sinh 9z)`

Differentiate w. r. t. z to get:

`\begin{gathered} (dy)/(dz)=(d)/(dz)(\ln \sinh 9z) \\ =(1)/(\sinh9z)(d)/(dz)(\sinh 9z) \\ =(1)/(\sinh9z)\cosh 9z((d)/(dz)9z) \\ =(9\cosh 9z)/(\sinh 9z) \\ =9\cot h9z \end{gathered}`

Hence the derivative is 9cot9z.