derivative of ax^3+bx^2-c/3 x+d

解

\frac{d}{d x} (a x^{3} + b x^{2} - \frac{c}{3} x + d)

3 a x^{2} + 2 b x - \frac{c}{3}

解答ステップ

\frac{d}{d x} (a x^{3} + b x^{2} - \frac{c}{3} x + d)

簡素化

a x^{3} + b x^{2} - \frac{c}{3} x + d : a x^{3} + b x^{2} - \frac{c x}{3} + d

= \frac{d}{d x} (a x^{3} + b x^{2} - \frac{c x}{3} + d)

和/差の法則を適用:

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

= \frac{d}{d x} (a x^{3}) + \frac{d}{d x} (b x^{2}) - \frac{d}{d x} (\frac{c x}{3}) + \frac{dd}{d x}

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

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

\frac{d}{d x} (\frac{c x}{3}) = \frac{c}{3}

\frac{dd}{d x} = 0

= 3 a x^{2} + 2 b x - \frac{c}{3} + 0

簡素化

= 3 a x^{2} + 2 b x - \frac{c}{3}