Find the derivative of y.
-$$y = \cosh x ^ { 5 }$$
A) $\sinh x ^ { 5 }$
B) $- 5 x ^ { 4 } \sinh x ^ { 5 }$
C) $5 x ^ { 4 } \sinh x ^ { 5 }$
D) $- \sinh x ^ { 5 }$

Question

Quizplus · Accepted Answer

Using the chain rule, we have:
$$\frac{dy}{dx} = 5\cosh x^4\cdot \sinh x$$
Since $\cosh x^4 = \frac{1}{2}\left[\left(e^{x^4}\right) + \left(e^{-x^4}\right)\right]$ and $\sinh x = \frac{1}{2}\left[\left(e^{x}\right) - \left(e^{-x}\right)\right]$, we can simplify the expression as:
$$\frac{dy}{dx} = \frac{5}{2}\left[\left(e^{x^4 + x}\right) - \left(e^{x^4 - x}\right)\right]$$
which can also be written as:
$$\frac{dy}{dx} = \boxed{(C) \: 5x^4\sinh x^5}$$

Find the Derivative of Y y=cosh⁡x5y = \cosh x ^ { 5 }y=coshx5

Find the Derivative of Y $y = \cosh x ^ { 5 }$