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Popular >

derivative of e^{1/(x^3})

Solution

\frac{d}{d x} (e^{\frac{1}{x ^{3}}})

Solution

- \frac{3 e ^{\frac{1}{x ^{3}}}}{x ^{4}}

Solution steps

\frac{d}{d x} (e^{\frac{1}{x ^{3}}})

Apply the chain rule:

e^{\frac{1}{x ^{3}}} \frac{d}{d x} (\frac{1}{x ^{3}})

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

\frac{d}{d x} (\frac{1}{x ^{3}}) = - \frac{3}{x ^{4}}

= e^{\frac{1}{x ^{3}}} (- \frac{3}{x ^{4}})

Simplify

e^{\frac{1}{x ^{3}}} (- \frac{3}{x ^{4}}) : - \frac{3 e ^{\frac{1}{x ^{3}}}}{x ^{4}}

= - \frac{3 e ^{\frac{1}{x ^{3}}}}{x ^{4}}

Popular Examples

(dy)/(dx)y=(y+1)(2x+1),y(-1)=1

\frac{d y}{d x} y = (y + 1) (2 x + 1), y (- 1) = 1

integral of z^2(z^3-1)^6

\int z^{2} (z^{3} - 1)^{6} d z

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\int p (p + 6)^{5} d p

integral of 2/(1-4x^2)

\int \frac{2}{1 - 4 x ^{2}} d x

tangent of f(x)=2x-x^2,\at x=1 tangent of

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Frequently Asked Questions (FAQ)

What is the derivative of e^{1/(x^3}) ?
The derivative of e^{1/(x^3}) is -(3e^{1/(x^3)})/(x^4)
What is the first derivative of e^{1/(x^3}) ?
The first derivative of e^{1/(x^3}) is -(3e^{1/(x^3)})/(x^4)