Question

Найти производную функции. 1)У=х^4 ; 2) у=5х^3 ; 3)у=х2+9х 4) у=1+х^2/3х

Answer 1

1) y´=4x³

2)y´=5.3.x²=15x²

3)y´= (x²)´+(9x)´=2x+9

4)y´=((1+x²)´.3x - (1+x²).(3x)´)/(3x)²=(2x.3x -(1+x²).3)/(3x²)=

=(6x²-3-3x²)/(3x)²=(3x²-3)/(3x)²=3(x²-1)/9x²=(x²-1)/3x² , x≠0