Question

Помогите найти производную

Answer 1

1)у=2х-х³
у'=2-3х²
2)у=-3х²+√х
у'=-6х+1/(2√х)
3)у=2х^3/2
у'=3х^1/2=3√х
4)у=2/5х²
у'=(2'(5х²)-2*(5х²)')/(5х²)²=-4/5х²
5)у=7х²/(3х²-2)
у'=((7х²)'*(3х²-2)-(3х²-2)'*(7х²))/(3х²-2)²=(42х³-28х-42х³)/(3х²-2)²=-28х/(3х²-2)
6)у=sinx+2^x
y'=cosx+2^xln2
7)y=4lnX+√x
y'=4/x+1/2√x
8)y=(5x²+1)(x³+x)=5x^5+x³+5x³+x=5x^5+6x³+x
y'=25x⁴+18x²+1
9)y=x⁴/√x
y=((x⁴)'√x-(√x)'x⁴)/x=4x³√x-x⁴/2√x