derivative of (6x-7^3(8x^2+9)^2)

解

\frac{d}{d x} ((6 x - 7)^{3} (8 x^{2} + 9)^{2})

18 (6 x - 7)^{2} (8 x^{2} + 9)^{2} + 32 x (8 x^{2} + 9) (6 x - 7)^{3}

解答ステップ

\frac{d}{d x} ((6 x - 7)^{3} (8 x^{2} + 9)^{2})

積の法則を適用:

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

f = (6 x - 7)^{3}, g = (8 x^{2} + 9)^{2}

= \frac{d}{d x} ((6 x - 7)^{3}) (8 x^{2} + 9)^{2} + \frac{d}{d x} ((8 x^{2} + 9)^{2}) (6 x - 7)^{3}

\frac{d}{d x} ((6 x - 7)^{3}) = 18 (6 x - 7)^{2}

\frac{d}{d x} ((8 x^{2} + 9)^{2}) = 32 x (8 x^{2} + 9)

= 18 (6 x - 7)^{2} (8 x^{2} + 9)^{2} + 32 x (8 x^{2} + 9) (6 x - 7)^{3}