derivative of x^2sqrt(8x-5)

解

\frac{d}{d x} (x^{2} 8 x - 5)

\frac{20 x ^{2} - 10 x}{8 x - 5}

解答ステップ

\frac{d}{d x} (x^{2} 8 x - 5)

積の法則を適用:

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

f = x^{2}, g = 8 x - 5

= \frac{d}{d x} (x^{2}) 8 x - 5 + \frac{d}{d x} (8 x - 5) x^{2}

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

\frac{d}{d x} (8 x - 5) = \frac{4}{8 x - 5}

= 2 x 8 x - 5 + \frac{4}{8 x - 5} x^{2}

簡素化

2 x 8 x - 5 + \frac{4}{8 x - 5} x^{2} : \frac{20 x ^{2} - 10 x}{8 x - 5}

= \frac{20 x ^{2} - 10 x}{8 x - 5}