Question

Решите производную.....

Answer 1

$y(t)=sqrt{t}; (sqrt[3]{t}+2t)=sqrt[6]{x^5}+2t^{3/2}\\y'(t)=frac{5}{6}cdot t^{-frac{1}{6}}+3cdot t^{frac{1}{2}}=frac{5}{6sqrt[6]{t}}+3sqrt{t}\\\f(x)=frac{(1+x^2)(2x+3)}{(1+sqrt{x})^2}=frac{2x^3+2x+3x^2+3}{(1+sqrt{x})^2}\\f'(x)=frac{(6x^2+2+6x)(1+sqrt{x})^2-(2x^3+3x^2+2x+3)cdot 2(1+sqrt{x})cdot frac{1}{2sqrt{x}}}{(1+sqrt{x})^4}=\\=frac{sqrt{x}(6x^2+6x+2)(1+sqrt{x})^2-(2x^3+3x^2+2x+3)cdot (1+sqrt{x})}{sqrt{x}cdot (1+sqrt{x})^4}$