What is the derivative of (e^{x/2}/(x+1)) ?

The derivative of (e^{x/2}/(x+1)) is (e^{x/2}x-e^{x/2})/(2(x+1)^2)

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

The first derivative of (e^{x/2}/(x+1)) is (e^{x/2}x-e^{x/2})/(2(x+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{sin ( x )}{cos ( x ) + sin ( x )} d x

\int \frac{e ^{8 x}}{e ^{16 x} + 16} d x

\int_{1}^{4} \frac{6}{x ^{2}} d x

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

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

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