derivative sqrt(x)(8x+5)^4

解

導関数

x (8 x + 5)^{4}

\frac{( 8 x + 5 ) ^{4}}{2 x} + 32 x (8 x + 5)^{3}

解答ステップ

\frac{d}{d x} (x (8 x + 5)^{4})

積の法則を適用:

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

f = x, g = (8 x + 5)^{4}

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

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

\frac{d}{d x} ((8 x + 5)^{4}) = 32 (8 x + 5)^{3}

= \frac{1}{2 x} (8 x + 5)^{4} + 32 (8 x + 5)^{3} x

\frac{1}{2 x} (8 x + 5)^{4} = \frac{( 8 x + 5 ) ^{4}}{2 x}

= \frac{( 8 x + 5 ) ^{4}}{2 x} + 32 x (8 x + 5)^{3}