Question

Найдите производную функций 1) y=x*sinx 2) y=√(x^2+8x-2)

Answer 1

$1)\; \; y=x\cdot sinx\\\\y'=x'\cdot sinx+x\cdot (sinx)'=sinx+x\cdot cosx\\\\2)\; \; y= \sqrt{x^2+8x-2}\; ,\qquad (\sqrt{u})'=\frac{1}{2\sqrt{u}}\cdot u'\\\\y'= \frac{1}{2\sqrt{x^2+8x-2}} \cdot (x^2+8x-2)'= \frac{1}{2\sqrt{x^2+8x-2}} \cdot (2x+8)= \frac{x+4}{\sqrt{x^2+8x-2}}$

$P.S.\quad \\\\(\sqrt{u})'=\frac{1}{2\sqrt{u}}\cdot u'\\\\(\sqrt{x})'=\frac{1}{2\sqrt{x}}\cdot \underbrace {x'}_{1}=\frac{1}{2\sqrt{x}}$