derivative f(x)=(x+1)^2(x-4)^3

Решение

производное от

f (x) = (x + 1)^{2} (x - 4)^{3}

2 (x + 1) (x - 4)^{3} + 3 (x - 4)^{2} (x + 1)^{2}

Шаги решения

\frac{d}{d x} ((x + 1)^{2} (x - 4)^{3})

Производная произведения:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x + 1)^{2}, g = (x - 4)^{3}

= \frac{d}{d x} ((x + 1)^{2}) (x - 4)^{3} + \frac{d}{d x} ((x - 4)^{3}) (x + 1)^{2}

\frac{d}{d x} ((x + 1)^{2}) = 2 (x + 1)

\frac{d}{d x} ((x - 4)^{3}) = 3 (x - 4)^{2}

= 2 (x + 1) (x - 4)^{3} + 3 (x - 4)^{2} (x + 1)^{2}