Question

Найти производную функции
1) y=-6x+4) ^5
2) y=x^2+1/2x^2-1

Answer 1

1) y'=5*(-6)*(-6x+4)⁴=-30(-6x+4)⁴

2) y'=(x²+1/(2x²)-1)'=2x-(1/x³)

Answer 2

Ответ:

$1)\ \ y=(-6x+4)^5\\\\y'=5(-6x+4)^4\cdot (-6x+4)'=5(-6x+4)^4\cdot (-6)=-30\cdot (4-6x)^4\\\\\\2)\ \ y=\dfrac{x^2+1}{2x^2-1}\\\\y'=\dfrac{2x(2x^2-1)-4x(x^2+1)}{(2x^2-1)^2}=\dfrac{-6x}{(2x^2-1)^2}\\\\\\\star \ \ y=x^2+\dfrac{1}{2x^2}-1\ \ ,\ \ y'=2x-\dfrac{4x}{4x^4}=2x-\dfrac{1}{x^3}\ \ \star$