Question

Найдите производную функции:
3)$frac{1}{x^{2} }$ -$sqrt{x}$

Answer 1

$frac{d}{dx}(frac{1}{x^2}-sqrt{x})=\\=frac{d}{dx}(frac{1}{x^2})-frac{d}{dx}(sqrt{x})=\\=frac{d}{dx}(x^{-2})-frac{d}{dx}(x^{frac{1}{2}})=\\=-2x^{-3}-frac{1}{2}x^{-frac{1}{2}}=\\=-frac{2}{x^3}-frac{1}{2sqrt{x}}=\\=-frac{2cdot :2sqrt{x}}{x^3cdot :2sqrt{x}}-frac{1cdot :x^{frac{5}{2}}sqrt{x}}{2sqrt{x}x^{frac{5}{2}}sqrt{x}}=\\=-frac{4sqrt{x}}{2x^3sqrt{x}}-frac{x^{frac{5}{2}}sqrt{x}}{2x^3sqrt{x}}=\\=frac{-4sqrt{x}-x^{frac{5}{2}}sqrt{x}}{2x^3sqrt{x}}=$

$=-frac{sqrt{x}left(4+x^{frac{5}{2}}right)}{2x^3sqrt{x}}=\\=-frac{x^{frac{1}{2}}left(x^{frac{5}{2}}+4right)}{2x^3sqrt{x}}=\\=-frac{x^{frac{5}{2}}+4}{2sqrt{x}x^{-frac{1}{2}+3}}=\\=-frac{x^{frac{5}{2}}+4}{2x^{frac{5}{2}}sqrt{x}}$