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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 5 tan (3 x)

n = 1 \sum \infty \frac{n - 5}{n + 2}

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

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

\frac{d}{d x} (\frac{4 x}{e ^{x}})

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