derivative of 2(3^{-x}^2+log_{2}(x^4-1))

解

\frac{d}{d x} (2 (3^{- x})^{2} + lo g_{2} (x^{4} - 1))

- 4 ln (3) \cdot 9^{- x} + \frac{4 x ^{3}}{ln ( 2 ) ( x ^{4} - 1 )}

解答ステップ

\frac{d}{d x} (2 (3^{- x})^{2} + lo g_{2} (x^{4} - 1))

簡素化

2 (3^{- x})^{2} + lo g_{2} (x^{4} - 1) : 2 \cdot 9^{- x} + lo g_{2} (x^{4} - 1)

= \frac{d}{d x} (2 \cdot 9^{- x} + lo g_{2} (x^{4} - 1))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 \cdot 9^{- x}) + \frac{d}{d x} (lo g_{2} (x^{4} - 1))

\frac{d}{d x} (2 \cdot 9^{- x}) = - 4 ln (3) \cdot 9^{- x}

\frac{d}{d x} (lo g_{2} (x^{4} - 1)) = \frac{4 x ^{3}}{ln ( 2 ) ( x ^{4} - 1 )}

= - 4 ln (3) \cdot 9^{- x} + \frac{4 x ^{3}}{ln ( 2 ) ( x ^{4} - 1 )}