derivative of x^2sqrt(4x-9)

解

\frac{d}{d x} (x^{2} 4 x - 9)

\frac{10 x ^{2} - 18 x}{4 x - 9}

解答ステップ

\frac{d}{d x} (x^{2} 4 x - 9)

積の法則を適用:

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

f = x^{2}, g = 4 x - 9

= \frac{d}{d x} (x^{2}) 4 x - 9 + \frac{d}{d x} (4 x - 9) x^{2}

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

\frac{d}{d x} (4 x - 9) = \frac{2}{4 x - 9}

= 2 x 4 x - 9 + \frac{2}{4 x - 9} x^{2}

簡素化

2 x 4 x - 9 + \frac{2}{4 x - 9} x^{2} : \frac{10 x ^{2} - 18 x}{4 x - 9}

= \frac{10 x ^{2} - 18 x}{4 x - 9}