Question

Допоможіть хто що хнає

Answer 1

$y=3x^3-7x^2-2x+4\\y'=9x^2-14x-2$

$y=6x^5-\cos x\\y'=30x^4-(-\sin x)=30x^4+\sin x$

$y=\dfrac 1x +\sin x-x^3\\y'=-\dfrac {1}{x^2}+\cos x-3x^2$

$y=x^3 \sin x\\y'=3x^2\sin x+x^3 \cos x$

$y=(4x-5)(2x+1)=8x^2-10x+4x-5=8x^2-6x-5\\y'=16x-6$

$y=\dfrac{4x-1}{2x+3}\\y'=\dfrac{(4x-1)' \cdot (2x+3)-(4x-1) \cdot (2x+3)'}{(2x+3)^2}=\dfrac{4 \cdot (2x+3) -2 \cdot (4x-1)}{(2x+3)^2}=\\}=\dfrac{8x+12-8x+2}{(2x+3)^2}=\dfrac{14}{(2x+3)^2}$

$y=\dfrac{x^2}{x+5}\\y'=\dfrac{(x^2) ' \cdot (x+5)-x^2 \cdot (x+5)'}{(x+5)^2}=\dfrac{2x (x+5)-x^2}{(x+5)^2}=\\=\dfrac{2x^2+10x-x^2}{(x+5)^2}=\dfrac{x^2+10x}{(x+5)^2}$