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人気のある微分積分 >

derivative f(x)=x^2*sin(x)

解

導関数

f (x) = x^{2} \cdot sin (x)

解

2 x sin (x) + cos (x) x^{2}

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = sin (x)

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

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

\frac{d}{d x} (sin (x)) = cos (x)

= 2 x sin (x) + cos (x) x^{2}

グラフ

人気の例

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