derivative f(x)=x^2*(x^3+2)

解

導関数

f (x) = x^{2} \cdot (x^{3} + 2)

5 x^{4} + 4 x

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = x^{3} + 2

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

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

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

= 2 x (x^{3} + 2) + 3 x^{2} x^{2}

簡素化

2 x (x^{3} + 2) + 3 x^{2} x^{2} : 5 x^{4} + 4 x

= 5 x^{4} + 4 x