Question

Найдите производные функций:
1) y=3x+$\frac{2}{x^{2} }$+1
2) y=(x-1)*tgx
3) y=3$x^{2}$-$\frac{2}{x}$+2$\sqrt{x}$

Answer 1

Производная равна 3-(2/х)

y'=(x-1)'*tgx+(x-1)*tg'x=tgx+(x-1)*(1/cos²x)

6x+2/x²+2*1/2√x=6x+2/x²+1/√x

Answer 2

$1)\; \; y=3x+\frac{2}{x^2}+1=3x+2\cdot x^{-2}+1\\\\y'=3+2\cdot (-2)\cdot x^{-3}+0=3-\frac{4}{x^3}\\\\\\2)\; \; y=(x-1)\cdot tgx\\\\y'=tgx+(x-1)\cdot \frac{1}{cos^2x}\\\\\\3)\; \; y=3x^2-\frac{2}{x}+2\sqrt{x}=3x^2-2\cdot x^{-1}+2\sqrt{x}\\\\y'=6x-2\cdot (-1)\cdot x^{-2}+2\cdot \frac{1}{2\sqrt{x}}=6x+\frac{2}{x^2}+\frac{1}{\sqrt{x} }$