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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (t) = - 2

x \to 0 lim (\frac{0}{x ^{6}})

y = x^{2} + 2 x

x \to 0 lim (x ln (x^{2}))

x \to \infty lim (e^{a x})

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