Question

Решите производную.....

Answer 1

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