Question

# Find the derivatives of the following function with respect to x and simplify the result. y=\cos h(\log x)

Derivatives
Find the derivatives of the following function with respect to x and simplify the result.
$$\displaystyle{y}={\cos{{h}}}{\left({\log{{x}}}\right)}$$

2021-05-26
Step 1
To find the derivative of hyperbolic function with respect to x
Use chain rule
Step 2
$$\displaystyle{y}={\cos{{h}}}{\left({\log{{x}}}\right)}$$
$$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({\cos{{h}}}{\left({\log{{x}}}\right)}\right)}$$
$$\displaystyle={\sin{{h}}}{\left({\log{{x}}}\right)}\cdot{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({\log{{x}}}\right)}$$
$$\displaystyle={\sin{{h}}}{\left({\log{{x}}}\right)}\cdot{\left({\frac{{{1}}}{{{x}}}}\right)}$$