Question

Очень срочно пожалуйста!

Answer 1

$1)\ \ y=x(x^2-5x+1)=x^3-5x^2+x\\\\y'=3x^2-10x+1\\\\\\2)\ \ y=\dfrac{x^3-5x^2+1}{x^2}=x-5+\dfrac{1}{x^2}\\\\y'=1-\dfrac{2x}{x^4}=1-\dfrac{2}{x^3}=\dfrac{x^3-2}{x^3}\\\\\\3)\ \ y=x\cdot cosx\\\\y'=cosx-x\cdot sinx$

$4)\ \ y=(x^3-5x+1)^5\\\\y'=5(x^3-5x+1)^4\cdot (3x^2-5)\\\\\\5)\ \ y=sin\Big(4x-\dfrac{\pi}{4}\Big)\\\\y'=cos\Big(4x-\dfrac{\pi}{4}\Big)\cdot \Big(4x-\dfrac{\pi}{4}\Big)'=4\cdot cos\Big(4x-\dfrac{\pi}{4}\Big)$