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Popular >

derivative of \sqrt[x]{e}

Solution

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

Solution

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

Solution steps

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

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}}

Graph

Popular Examples

integral of 8/(sec(2x)-1)

\int \frac{8}{sec ( 2 x ) - 1} d x

(\partial)/(\partial x)(sin(xy)z^2)

\frac{\partial}{\partial x} (sin (x y) z^{2})

tangent of y=(-4x)/(x^2+1),(0,0)tangent of

y = \frac{- 4 x}{x ^{2} + 1}, (0, 0)

x y^{^{'}} - 4 y = - 2 x

(\partial)/(\partial x)(xarccos(x))

\frac{\partial}{\partial x} (x arccos (x))

Frequently Asked Questions (FAQ)

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