derivative of a^2x+a^2y+b^2x+b^2y

解

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

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

解答ステップ

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

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

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