What is the derivative of (-e^xx+2e^x/((1-x)^2)) ?

The derivative of (-e^xx+2e^x/((1-x)^2)) is (e^x(x^2-4x+5))/((1-x)^3)

What is the first derivative of (-e^xx+2e^x/((1-x)^2)) ?

The first derivative of (-e^xx+2e^x/((1-x)^2)) is (e^x(x^2-4x+5))/((1-x)^3)

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

\frac{e ^{x} ( x ^{2} - 4 x + 5 )}{( 1 - x ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( - e ^{x} x + e ^{x} ) ( 1 - x ) ^{2} - ( - 2 ( 1 - x ) ) ( - e ^{x} x + 2 e ^{x} )}{( ( 1 - x ) ^{2} ) ^{2}} : \frac{e ^{x} ( x ^{2} - 4 x + 5 )}{( 1 - x ) ^{3}}

= \frac{e ^{x} ( x ^{2} - 4 x + 5 )}{( 1 - x ) ^{3}}

sin (3 x), \frac{π}{3}

\frac{d y}{d x} = \frac{x}{y ^{2} 1 + x}

\int 2 e^{2 y} d y

\int_{- 12}^{0} \frac{1}{4 - x} d x

\frac{\partial}{\partial x} (x \cdot arctan (\frac{y}{x}))

What is the derivative of (-e^xx+2e^x/((1-x)^2)) ?
The derivative of (-e^xx+2e^x/((1-x)^2)) is (e^x(x^2-4x+5))/((1-x)^3)
What is the first derivative of (-e^xx+2e^x/((1-x)^2)) ?
The first derivative of (-e^xx+2e^x/((1-x)^2)) is (e^x(x^2-4x+5))/((1-x)^3)