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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches-2 of \sqrt[3]{x+2}cos(5/((x+2)^2))

integral from-1 to 1 of 1/(x^2+1)

\int_{- 1}^{1} \frac{1}{x ^{2} + 1} d x

y^{''}+4y=-4sec(2t)

y^{^{''}} + 4 y = - 4 sec (2 t)

x^{''}+4x^'+5x=0

x^{^{''}} + 4 x^{^{'}} + 5 x = 0

(\partial)/(\partial n)(nm)

\frac{\partial}{\partial n} (nm)

Frequently Asked Questions (FAQ)

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