What is the derivative of (e^{2-x}-2x/(e^{2-x)+3x}) ?

The derivative of (e^{2-x}-2x/(e^{2-x)+3x}) is (-5e^{-x+2}x-5e^{-x+2})/((e^{2-x)+3x)^2}

What is the first derivative of (e^{2-x}-2x/(e^{2-x)+3x}) ?

The first derivative of (e^{2-x}-2x/(e^{2-x)+3x}) is (-5e^{-x+2}x-5e^{-x+2})/((e^{2-x)+3x)^2}

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

\frac{- 5 e ^{- x + 2} x - 5 e ^{- x + 2}}{( e ^{2 - x} + 3 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

= \frac{( - e ^{2 - x} - 2 ) ( e ^{2 - x} + 3 x ) - ( - e ^{2 - x} + 3 ) ( e ^{2 - x} - 2 x )}{( e ^{2 - x} + 3 x ) ^{2}}

Expand

(- e^{2 - x} - 2) (e^{2 - x} + 3 x) - (- e^{2 - x} + 3) (e^{2 - x} - 2 x) : - 5 e^{- x + 2} x - 5 e^{- x + 2}

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

\int x^{2} e^{13 x} d x

x \to 8 lim (\frac{1}{( x - 8 )})

\frac{\partial}{\partial y} ((2 - x) (y - 2) (3 - x - y))

\int π (2 y)^{2} d y

- \frac{50}{t ^{3}} + \frac{5}{t ^{2}}

What is the derivative of (e^{2-x}-2x/(e^{2-x)+3x}) ?
The derivative of (e^{2-x}-2x/(e^{2-x)+3x}) is (-5e^{-x+2}x-5e^{-x+2})/((e^{2-x)+3x)^2}
What is the first derivative of (e^{2-x}-2x/(e^{2-x)+3x}) ?
The first derivative of (e^{2-x}-2x/(e^{2-x)+3x}) is (-5e^{-x+2}x-5e^{-x+2})/((e^{2-x)+3x)^2}