Question

Найдите производные функций:
1. f(x)=(x^3+x^2+x)*(x-2)
2.y=lg√x^2+4
3.y=x/e^2x

Answer 1

1) f ' (x)=(x^3+x^2+x)' *(x-2)+(x^3+x^2+x)*(x-2)'=(3x^2+2x+1)*(x-2)+(x^3+x^2+x)=3x^3+2x^2+x-6x^2-4x-2=3x^3-4x^2-4x-2

Answer 2

2) у'(x)=2x*(1/(2Vx^2+4))*(1/(1/(2Vx^2+4)*ln10)=x((2Vx^2+4)*ln10)/Vx^2+4=xln10*2=2x*ln10

Answer 3

3) у'(x)=(e^2x-x(2*e^2x))/(e^2x)^2=(e^2x-2x*e^2x)/e^4x^2