Question

Вычислите производные функции
а)f(x)=4x^5-5x^8+15
б)f(x)=(x^2-x)×x
в)f(x)=x^3/x+1

Answer 1

а)f'(x)=4×5x^4-5×8x^7=20x^4-40x^7
б)f'(x)=(x²-x)'×x+(x²-x)×(x)'=(2x-1)×x+x²-x=2x²-x+x²-x=3x²-2x
в)f'(x)=[(x³)'(x+1)-x³(x+1)']/(x+1)²=[3x²(x+1)-x³]/(x+1)²=(2x³+3x²)/(x+1)²