derivative f(x)=x^2sqrt(4x-1)

解

導関数

f (x) = x^{2} 4 x - 1

\frac{10 x ^{2} - 2 x}{4 x - 1}

解答ステップ

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

積の法則を適用:

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

f = x^{2}, g = 4 x - 1

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

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

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

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

簡素化

2 x 4 x - 1 + \frac{2}{4 x - 1} x^{2} : \frac{10 x ^{2} - 2 x}{4 x - 1}

= \frac{10 x ^{2} - 2 x}{4 x - 1}