Question

fʼ(π)=? если f(x)=(3x²•e^sinx)-8​

Answer 1

$f(x)=3x^2\cdot e^{\sin x}-8$

$f'(x)=(3x^2\cdot e^{\sin x}-8)'=(3x^2)'\cdot e^{\sin x}+3x^2\cdot (e^{\sin x})'-(8)'=$

$=3\cdot2x\cdot e^{\sin x}+3x^2\cdot e^{\sin x}\cdot(\sin x)'-0=6x\cdot e^{\sin x}+3x^2\cdot e^{\sin x}\cdot\cos x=$

$=(6x+3x^2\cos x)\cdot e^{\sin x}$

$f'(\pi)=(6\pi+3\pi^2\cos \pi)\cdot e^{\sin \pi}=(6\pi+3\pi^2\cdot(-1))\cdot e^{0}=$

$=(6\pi-3\pi^2)\cdot 1=6\pi-3\pi^2$

Ответ: $6\pi-3\pi^2$