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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{1 - t ^{2}}{t ^{4}} d t

\int 10 ln (x^{2} - 1) d x

\frac{2 x - 6}{x + 1}, at x = 0

\frac{t}{t ^{2} + 36}

e^{x} \frac{d y}{d x} = 2

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