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

The derivative of (e^{2x}-1/(e^{2x)+1}) is (4e^{2x})/((e^{2x)+1)^2}

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

The first derivative of (e^{2x}-1/(e^{2x)+1}) is (4e^{2x})/((e^{2x)+1)^2}

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

\frac{4 e ^{2 x}}{( e ^{2 x} + 1 ) ^{2}}

Solution steps

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

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

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

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

Expand

2 e^{2 x} (e^{2 x} + 1) - 2 e^{2 x} (e^{2 x} - 1) : 4 e^{2 x}

= \frac{4 e ^{2 x}}{( e ^{2 x} + 1 ) ^{2}}

y^{^{''}} + 14 y^{^{'}} + 100 y = 10 sin (2 π \cdot x) + 5 sin (π \cdot x)

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

3 y^{^{''}} + y^{^{'}} + 2 y = 0

\int \frac{4 x ^{2}}{x ^{3} + 8} d x

\frac{\partial}{\partial x} ((1 - x - 4 y)^{\frac{1}{2}})

What is the derivative of (e^{2x}-1/(e^{2x)+1}) ?
The derivative of (e^{2x}-1/(e^{2x)+1}) is (4e^{2x})/((e^{2x)+1)^2}
What is the first derivative of (e^{2x}-1/(e^{2x)+1}) ?
The first derivative of (e^{2x}-1/(e^{2x)+1}) is (4e^{2x})/((e^{2x)+1)^2}