derivative of (2x+e^x(5-sqrt(x)))

解

\frac{d}{d x} ((2 x + e^{x}) (5 - x))

\frac{- 6 x - 2 e ^{x} x + 10 e ^{x} x - e ^{x}}{2 x} + 10

解答ステップ

\frac{d}{d x} ((2 x + e^{x}) (5 - x))

積の法則を適用:

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

f = 2 x + e^{x}, g = 5 - x

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

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

\frac{d}{d x} (5 - x) = - \frac{1}{2 x}

= (2 + e^{x}) (5 - x) + (- \frac{1}{2 x}) (2 x + e^{x})

簡素化

(2 + e^{x}) (5 - x) + (- \frac{1}{2 x}) (2 x + e^{x}) : \frac{- 6 x - 2 e ^{x} x + 10 e ^{x} x - e ^{x}}{2 x} + 10

= \frac{- 6 x - 2 e ^{x} x + 10 e ^{x} x - e ^{x}}{2 x} + 10