Question

# Find the derivatives of the following functions. f(x)=x\tan h x

Derivatives
Find the derivatives of the following functions.
$$\displaystyle{f{{\left({x}\right)}}}={x}{\tan{{h}}}{x}$$

2021-05-06
Step 1 Let us find the derivative of given function
Given:
$$\displaystyle{f{{\left({x}\right)}}}={x}{\tan{{h}}}{x}$$
$$\displaystyle{f}'{\left({x}\right)}={x}{\tan{{h}}}{x}$$
$$\displaystyle{f}'{\left({x}\right)}={x}{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({\tan{{h}}}{x}\right)}+{\tan{{h}}}{x}{\frac{{{d}}}{{{\left.{d}{x}\right.}}}}{\left({x}\right)}$$
$$\displaystyle{f}'{\left({x}\right)}={x}{{\sec{{h}}}^{{{2}}}{x}}+{\tan{{h}}}{x}$$