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

The derivative of (e^{2x+1}/((x-1)^2)) is (2e^{2x+1}(x-2))/((x-1)^3)

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

The first derivative of (e^{2x+1}/((x-1)^2)) is (2e^{2x+1}(x-2))/((x-1)^3)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{1}{2} sin (2 x) d x

F (t) = 2 + 4 e^{- 4 t} - 3 e^{3 t}

\frac{\partial}{\partial x} (ln (x + \frac{y}{2 x}))

x \to \infty lim ((1 + \frac{7}{x})^{2 x})

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

What is the derivative of (e^{2x+1}/((x-1)^2)) ?
The derivative of (e^{2x+1}/((x-1)^2)) is (2e^{2x+1}(x-2))/((x-1)^3)
What is the first derivative of (e^{2x+1}/((x-1)^2)) ?
The first derivative of (e^{2x+1}/((x-1)^2)) is (2e^{2x+1}(x-2))/((x-1)^3)