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Popular >

derivative of e^{1/x}

Solution

derivative of

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

integral of 8x^3+12x+2

\int 8 x^{3} + 12 x + 2 d x

derivative of a{r}(xc,5x)

\frac{d}{d x} (a r (x) c, 5 x)

(\partial)/(\partial x)(x^2y^2-3y)

\frac{\partial}{\partial x} (x^{2} y^{2} - 3 y)

integral of 3x+2

\int 3 x + 2 d x

area f(x)=4x+8,0,8 area

f (x) = 4 x + 8, 0, 8

Frequently Asked Questions (FAQ)

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