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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to - 2 lim ((3 x - 8)^{2})

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

x \to 1 - lim (2 x - 2 - 2)

\frac{d}{d x} (x ln ∣ x ∣)

\frac{\partial}{\partial x} (x e^{2 y})

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