Question

Find derivatives for the functions. Assume a, b, c, and k are constants. f(x)=5x^{4}+\frac{1}{x^{2}}

Derivatives
ANSWERED
asked 2021-06-24
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({x}\right)}}}={5}{x}^{{{4}}}+{\frac{{{1}}}{{{x}^{{{2}}}}}}\)

Expert Answers (1)

2021-06-25

\(\displaystyle{f}'{\left({x}\right)}={5}{x}^{{{4}}}+{\frac{{{1}}}{{{x}^{{{2}}}}}}'\)
\(\displaystyle={5}{\left({x}^{{{4}}}\right)}'+{\left({x}^{{-{2}}}\right)}'\) Derivative of Sum
\(\displaystyle={20}{x}^{{{4}}}-{2}{x}^{{-{3}}}\) Power Rule

\(f'(x)=20x^{4}-\frac{2}{x^{3}}\)

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