Question

Будьте добры помогите с производными

Answer 1

Ответ.

$1.\ \ y=3x-5\ \ ,\ \ y'=3\\\\2.\ \y=2x^2-3x+6\ \ ,\ \ y'=4x-3\\\\3.\ \ y=-\dfrac{5}{x}\ \ ,\ \ y'=-\dfrac{-5}{x^2}=\dfrac{5}{x^2}\\\\4.\ \ y=x^3+6x^{-9}+3x+9\ \ ,\ \ y'=3x^2-54x^{-10}+3\\\\5.\ \ y=x^2+2x^{1/7}-2x^7+8\sqrt{x}\ \ ,\ \ y'=2x+\dfrac{2}{7}\, x^{-6/7}-14x^6+\dfrac{8}{2\sqrt{x}}\\\\6.\ \y=2sinx-cosx+e^{x}\ \ ,\ \ y'=2\, cosx+sinx+e^{x}\\\\7.\ \ y=(3x^2-x)(4x+7)=12x^3+17x^2-7x\ \ ,\ \ y'=36x^2+34x-7$

$8.\ y=\dfrac{x-5}{x^2-1}\ \ ,\ \ y'=\dfrac{x^2-1-(x-5)\cdot 2x}{(x^2-1)^2}=\dfrac{-x^2+10x-1}{(x^2-1)^2}\\\\\\9.\ y=2x^3-0,3x+5\ \ ,\ \ y'=6x-0,3\\\\10.\ y=-4e^{x}+3^{x}-12\ \ ,\ \ y'=-4e^{x}+3^{x}\cdot ln3$