Question

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

Derivatives
ANSWERED
asked 2021-06-22
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{h}{\left({w}\right)}={w}^{{{3}}}{\ln{{\left({10}{w}\right)}}}\)

Answers (1)

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