derivative of 5x^3y^4

解

\frac{d}{d x} (5 x^{3} y^{4})

5 (3 x^{2} y^{4} + 4 y^{3} \frac{d y}{d x} x^{3})

解答ステップ

\frac{d}{d x} (5 x^{3} y^{4})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{d}{d x} (x^{3} y^{4})

積の法則を適用:

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

f = x^{3}, g = y^{4}

= 5 (\frac{d}{d x} (x^{3}) y^{4} + \frac{d}{d x} (y^{4}) x^{3})

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

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

= 5 (3 x^{2} y^{4} + 4 y^{3} \frac{d y}{d x} x^{3})