Question

Oblicz pochodną (x²-x)²(x³-1)²

Answer 1

Odpowiedź:

[f(x)g(x)]'=f'(x)g(x)+g'(x)f(x)

f(x)=(x²-x)²

g(x)=(x³-1)²

f'(x)=2(x²-x)*(2x-1)

g'(x)=2(x³-1)*3x²=6x²(x³-1)

[(x²-x)²(x³-1)²]'=2(x²-x)*(2x-1)*(x³-1)²+6x²(x³-1)*(x²-x)²=2x(x-1)(x³-1)[(2x-1)(x³-1)+

+3x²*x(x-1)]=2x(x-1)(x³-1)(2x⁴-2x-x³+1+3x⁴-3x³)=2x(x-1)(x³-1)(5x⁴-4x³-2x+1)