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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int tan (b) x d x

f (x) = tan (e^{x})

10 y^{^{''}} - 10 y^{^{'}} + 65 y = 0

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

f (x) = 4 x^{2} + 3

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