derivative of x^2sqrt(x-4)

解

\frac{d}{d x} (x^{2} x - 4)

\frac{5 x ^{2} - 16 x}{2 x - 4}

解答ステップ

\frac{d}{d x} (x^{2} x - 4)

積の法則を適用:

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

f = x^{2}, g = x - 4

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

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

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

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

簡素化

2 x x - 4 + \frac{1}{2 x - 4} x^{2} : \frac{5 x ^{2} - 16 x}{2 x - 4}

= \frac{5 x ^{2} - 16 x}{2 x - 4}