derivative of x^3sqrt(x-4)

解

\frac{d}{d x} (x^{3} x - 4)

\frac{7 x ^{3} - 24 x ^{2}}{2 x - 4}

解答ステップ

\frac{d}{d x} (x^{3} x - 4)

積の法則を適用:

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

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

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

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

\frac{d}{d x} (x - 4) = \frac{1}{2 x - 4}

= 3 x^{2} x - 4 + \frac{1}{2 x - 4} x^{3}

簡素化

3 x^{2} x - 4 + \frac{1}{2 x - 4} x^{3} : \frac{7 x ^{3} - 24 x ^{2}}{2 x - 4}

= \frac{7 x ^{3} - 24 x ^{2}}{2 x - 4}