derivative x^2\sqrt[4]{4x-7}

解

導関数

x^{2} 4 4 x - 7

2 x 4 4 x - 7 + \frac{x ^{2}}{( 4 x - 7 ) ^{\frac{3}{4}}}

解答ステップ

\frac{d}{d x} (x^{2} 4 4 x - 7)

積の法則を適用:

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

f = x^{2}, g = 4 4 x - 7

= \frac{d}{d x} (x^{2}) 4 4 x - 7 + \frac{d}{d x} (4 4 x - 7) x^{2}

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

\frac{d}{d x} (4 4 x - 7) = \frac{1}{( 4 x - 7 ) ^{\frac{3}{4}}}

= 2 x 4 4 x - 7 + \frac{1}{( 4 x - 7 ) ^{\frac{3}{4}}} x^{2}

\frac{1}{( 4 x - 7 ) ^{\frac{3}{4}}} x^{2} = \frac{x ^{2}}{( 4 x - 7 ) ^{\frac{3}{4}}}

= 2 x 4 4 x - 7 + \frac{x ^{2}}{( 4 x - 7 ) ^{\frac{3}{4}}}