KolstenB559612 KolstenB559612
  • 03-11-2022
  • Mathematics
contestada

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

Respuesta :

RhonanZ165384 RhonanZ165384
  • 03-11-2022

The given function is:

[tex]y=\ln (\sinh 9z)[/tex]

Differentiate w. r. t. z to get:

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

Hence the derivative is 9cot9z.

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