What is the derivative of (8-xe^x/(x+e^x)) ?

The derivative of (8-xe^x/(x+e^x)) is (-e^xx^2-e^{2x}-8e^x-8)/((x+e^x)^2)

What is the first derivative of (8-xe^x/(x+e^x)) ?

The first derivative of (8-xe^x/(x+e^x)) is (-e^xx^2-e^{2x}-8e^x-8)/((x+e^x)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{8 - x e ^{x}}{x + e ^{x}})

\frac{- e ^{x} x ^{2} - e ^{2 x} - 8 e ^{x} - 8}{( x + e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 - x e ^{x}}{x + e ^{x}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 - x e ^{x} ) ( x + e ^{x} ) - \frac{d}{d x} ( x + e ^{x} ) ( 8 - x e ^{x} )}{( x + e ^{x} ) ^{2}}

\frac{d}{d x} (8 - x e^{x}) = - e^{x} x - e^{x}

\frac{d}{d x} (x + e^{x}) = 1 + e^{x}

= \frac{( - e ^{x} x - e ^{x} ) ( x + e ^{x} ) - ( 1 + e ^{x} ) ( 8 - x e ^{x} )}{( x + e ^{x} ) ^{2}}

Expand

(- e^{x} x - e^{x}) (x + e^{x}) - (1 + e^{x}) (8 - x e^{x}) : - e^{x} x^{2} - e^{2 x} - 8 e^{x} - 8

= \frac{- e ^{x} x ^{2} - e ^{2 x} - 8 e ^{x} - 8}{( x + e ^{x} ) ^{2}}

4 y^{^{'}} = \frac{4 x y + 8 x ^{2} + 2 y ^{2}}{x ^{2}}

y^{^{'}} + csc (y) = 0

\int \frac{e ^{3 x} + 1}{e ^{x} + 1} d x

x \to 3 lim (2 x^{3} - 4 x - 10)

9 x^{2} x + 7 x^{2}

What is the derivative of (8-xe^x/(x+e^x)) ?
The derivative of (8-xe^x/(x+e^x)) is (-e^xx^2-e^{2x}-8e^x-8)/((x+e^x)^2)
What is the first derivative of (8-xe^x/(x+e^x)) ?
The first derivative of (8-xe^x/(x+e^x)) is (-e^xx^2-e^{2x}-8e^x-8)/((x+e^x)^2)