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Popular >

derivative of ((e^x))/(1+x)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches infinity of (x^4)/(e^{-6x)}

x \to \infty lim (\frac{x ^{4}}{e ^{- 6 x}})

area y=2ln(x),y=0,x=3e area

y = 2 ln (x), y = 0, x = 3 e

integral from 1 to-2 of (1/2)

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

inverse oflaplace 5/(s^2+5)inverse laplace

\frac{5}{s ^{2} + 5}

tangent of f(x)=1+2x-3x^2,\at x=0 tangent of

f (x) = 1 + 2 x - 3 x^{2}, at x = 0

Frequently Asked Questions (FAQ)

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