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

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