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Popular >

derivative of x/(3+e^x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

Popular Examples

integral of 2+x-x^2

\int 2 + x - x^{2} d x

integral of ((6x+7))/((x+2)^2)

\int \frac{( 6 x + 7 )}{( x + 2 ) ^{2}} d x

integral of (e^{4x})/(4-e^{4x)}

\int \frac{e ^{4 x}}{4 - e ^{4 x}} d x

integral of 5^{-x}

\int 5^{- x} d x

(\partial)/(\partial x)(y/(x^2(y+3)))

\frac{\partial}{\partial x} (\frac{y}{x ^{2} ( y + 3 )})

Frequently Asked Questions (FAQ)

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