derivative y=(3x^2-2x-4)5^x

解

導関数

y = (3 x^{2} - 2 x - 4) 5^{x}

(6 x - 2) \cdot 5^{x} + 5^{x} ln (5) (3 x^{2} - 2 x - 4)

解答ステップ

\frac{d}{d x} ((3 x^{2} - 2 x - 4) \cdot 5^{x})

積の法則を適用:

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

f = 3 x^{2} - 2 x - 4, g = 5^{x}

= \frac{d}{d x} (3 x^{2} - 2 x - 4) 5^{x} + \frac{d}{d x} (5^{x}) (3 x^{2} - 2 x - 4)

\frac{d}{d x} (3 x^{2} - 2 x - 4) = 6 x - 2

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

= (6 x - 2) \cdot 5^{x} + 5^{x} ln (5) (3 x^{2} - 2 x - 4)