How do you find the derivative of sinh^79(x)?

Mar 2, 2016

$79 {\sinh}^{78} \left(x\right) \cosh \left(x\right)$

Explanation:

According to the chain rule,

$\frac{d}{\mathrm{dx}} \left({u}^{79}\right) = 79 {u}^{78} \cdot u '$

So:

$\frac{d}{\mathrm{dx}} \left({\sinh}^{79} \left(x\right)\right) = 79 {\sinh}^{78} \left(x\right) \cdot \frac{d}{\mathrm{dx}} \left(\sinh \left(x\right)\right)$

$= 79 {\sinh}^{78} \left(x\right) \cosh \left(x\right)$