Question

Find the derivatives of the following function with respect to x and simplify the result. y=e^{x}\sin h x

Derivatives
Find the derivatives of the following function with respect to x and simplify the result.
$$\displaystyle{y}={e}^{{{x}}}{\sin{{h}}}{x}$$

2021-05-09

Step 1
$$\displaystyle{y}={e}^{{{x}}}{\sin{{h}}}{\left({x}\right)}$$
Apply product rule for taking derivative
$$y=uv$$
$$y'=u'v+v'(u)$$
derivative of $$\displaystyle{\sin{{h}}}{\left({x}\right)}\ {i}{s}\ {\cos{{h}}}{\left({x}\right)}$$
Step 2
$$\displaystyle{y}={e}^{{{x}}}{\sin{{h}}}{\left({x}\right)}$$
$$\displaystyle{y}'={e}^{{{x}}}{\sin{{h}}}{\left({x}\right)}+{e}^{{{x}}}{\cos{{h}}}{\left({x}\right)}$$
$$\displaystyle{y}'={e}^{{{x}}}{\left({\sin{{h}}}{\left({x}\right)}+{\cos{{h}}}{\left({x}\right)}\right)}$$