Question

Найдите производные функций по определению

Answer 1

$left(5-3x-x^2)'right|_{x_0}equivlimlimits_{hto0}dfrac{left(5-3x-x^2)right|_{x_0+h}-left(5-3x-x^2)right|_{x_0}}{h}=\=limlimits_{hto0}dfrac{(5-3(x_0+h)-(x_0+h)^2)-(5-3x_0-x_0^2)}h=\=limlimits_{hto0}dfrac{-3h-2x_0h-h^2}{h}=limlimits_{hto0}(-3-2x_0-h)=-3-2x_0$

$left.(sqrt{3-2x})'right|_{x_0}equivlimlimits_{hto0}dfrac{left.sqrt{3-2x}right|_{x_0+h}-left.sqrt{3-2x}right|_{x_0}}{h}=\=limlimits_{hto0}dfrac{sqrt{3-2x_0-2h}-sqrt{3-2x_0}}h=limlimits_{hto0}dfrac{(3-2x_0-2h)-(3-2x_0)}{h(sqrt{3-2x_0-2h}+sqrt{3-2x_0})}\ =limlimits_{hto0}dfrac{-2h}{h(sqrt{3-2x_0-2h}+sqrt{3-2x_0})}=\=-limlimits_{hto0}dfrac{2}{sqrt{3-2x_0-2h}+sqrt{3-2x_0}}=-dfrac{2}{sqrt{3-2x_0-0}+sqrt{3-2x_0}}=\=-dfrac1{sqrt{3-2x_0}}$