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Popular >

derivative of (e^x)/(2x+1)

Solution

derivative of

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

Solution

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

Solution steps

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

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

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

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

Expand

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

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

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Frequently Asked Questions (FAQ)

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