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人気のある微分積分 >

derivative of x^2y^5

解

\frac{d}{d x} (x^{2} y^{5})

解

2 x y^{5} + 5 y^{4} \frac{d y}{d x} x^{2}

解答ステップ

\frac{d}{d x} (x^{2} y^{5})

積の法則を適用:

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

f = x^{2}, g = y^{5}

= \frac{d}{d x} (x^{2}) y^{5} + \frac{d}{d x} (y^{5}) x^{2}

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

\frac{d}{d x} (y^{5}) = 5 y^{4} \frac{d y}{d x}

= 2 x y^{5} + 5 y^{4} \frac{d y}{d x} x^{2}

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