Question

# Find derivatives for the functions. Assume a, b, c, and k are constants. h(w)=w^{3}\ln(10w)

Derivatives
Find derivatives for the functions. Assume a, b, c, and k are constants.
$$\displaystyle{h}{\left({w}\right)}={w}^{{{3}}}{\ln{{\left({10}{w}\right)}}}$$

2021-06-23
$$\displaystyle{h}'{\left({w}\right)}={\left[{w}^{{{3}}}{\ln{{\left({10}{w}\right)}}}\right]}'$$
$$\displaystyle={\left[{w}^{{{3}}}\right]}'{\ln{{\left({10}{w}\right)}}}+{w}^{{{3}}}{\left[{\ln{{\left({10}{w}\right)}}}\right]}'$$
$$\displaystyle={3}{w}^{{{2}}}{\ln{{\left({10}{w}\right)}}}+{w}^{{{3}}}{\frac{{{1}}}{{{w}}}}$$
$$\displaystyle={3}{w}^{{{2}}}{\ln{{\left({10}{w}\right)}}}+{w}^{{{2}}}$$