Question

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

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

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