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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

y - x y^{^{'}} = a (1 + x^{2} y^{^{'}})

x \to 3 lim (\frac{2 x - 9}{x - 3})

\frac{\partial}{\partial x} (x^{3} y z^{2} + 8 yz)

\int \frac{1}{cos ^{2} ( x ) + 5 cos ( x ) + 6} d x

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