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Popular >

derivative of f(x)=e^{1/x}

Solution

derivative of

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

Solution

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

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

Simplify

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

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

Popular Examples

midpoint (7,-12),(-5,-15)midpoint

(7, - 12), (- 5, - 15)

cartesian (-3,-pi/6)polar to cartesian

(- 3, - \frac{π}{6})

midpoint (-2,-7),(7,4)midpoint

(- 2, - 7), (7, 4)

midpoint (3,17),(-14,-8)midpoint

(3, 17), (- 14, - 8)

line θ=(4pi)/3 line

θ = \frac{4 π}{3}

Frequently Asked Questions (FAQ)

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