derivative of x(2x+3^4)

解

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

(2 x + 3)^{4} + 8 x (2 x + 3)^{3}

解答ステップ

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

積の法則を適用:

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

f = x, g = (2 x + 3)^{4}

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

\frac{d x}{d x} = 1

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

= 1 \cdot (2 x + 3)^{4} + 8 (2 x + 3)^{3} x

簡素化

= (2 x + 3)^{4} + 8 x (2 x + 3)^{3}