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

The derivative of e^{1/(sqrt(x)}) is -(e^{1/(sqrt(x))})/(2x^{3/2)}

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

The first derivative of e^{1/(sqrt(x)}) is -(e^{1/(sqrt(x))})/(2x^{3/2)}

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Popular >

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

- \frac{e ^{\frac{1}{x}}}{2 x ^{\frac{3}{2}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x^{- 2} (4 + 3 x^{- 3}))

\int (e^{x} - x^{e} + \frac{5}{x}) d x

\int 4^{7 x} d x

x \to - 1 lim (x + 5 - 2)

5^{x^{4}}

What is the derivative of e^{1/(sqrt(x)}) ?
The derivative of e^{1/(sqrt(x)}) is -(e^{1/(sqrt(x))})/(2x^{3/2)}
What is the first derivative of e^{1/(sqrt(x)}) ?
The first derivative of e^{1/(sqrt(x)}) is -(e^{1/(sqrt(x))})/(2x^{3/2)}