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

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

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

\frac{2 e ^{x} x - 3 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 - 3 e^{x}

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

\frac{d ^{2}}{d x ^{2}} (2 x (x + 4)^{3})

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

\int \frac{x}{e ^{7} x} d x

\int_{0}^{\frac{π}{4}} 6 tan^{4} (x) d x

x \cdot arcsin (x)

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