derivative of x^2*y^2

解

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

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

解答ステップ

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

積の法則を適用:

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

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

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

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

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

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