Question

Find derivatives for the functions. Assume a, b, c, and k are constants. f(x)=\frac{1}{x^{2}}+5\sqrt{x}-7

Derivatives
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asked 2021-06-12
Find derivatives for the functions. Assume a, b, c, and k are constants.
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}^{{{2}}}}}}+{5}\sqrt{{{x}}}-{7}\)

Answers (1)

2021-06-13
Find derivative of given function:
\(\displaystyle{f}'{\left({x}\right)}=^{{{1}}}{\left({x}^{{-{2}}}\right)}'+{\left({5}{x}^{{{\frac{{{1}}}{{{2}}}}}}\right)}'-{7}'\)
\(\displaystyle=^{{{2}}}-{2}{x}^{{-{3}}}+{\frac{{{5}}}{{{x}}}}{x}^{{-{\frac{{{1}}}{{{2}}}}}}-{0}\)
\(\displaystyle=-{2}{x}^{{-{3}}}+{\frac{{{5}}}{{{2}}}}{x}^{{-{\frac{{{1}}}{{{2}}}}}}\)
Rules used:
(1) Derivative of sum
(2) Power rule
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