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Popular >

derivative of e^{4/x}

Solution

\frac{d}{d x} (e^{\frac{4}{x}})

Solution

- \frac{4 e ^{\frac{4}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (e^{\frac{4}{x}})

Apply the chain rule:

e^{\frac{4}{x}} \frac{d}{d x} (\frac{4}{x})

= e^{\frac{4}{x}} \frac{d}{d x} (\frac{4}{x})

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

= e^{\frac{4}{x}} (- \frac{4}{x ^{2}})

Simplify

e^{\frac{4}{x}} (- \frac{4}{x ^{2}}) : - \frac{4 e ^{\frac{4}{x}}}{x ^{2}}

= - \frac{4 e ^{\frac{4}{x}}}{x ^{2}}

Popular Examples

limit as x approaches 2 of 5x-6

x \to 2 lim (5 x - 6)

derivative of (4x-8/(x-5))

\frac{d}{d x} (\frac{4 x - 8}{x - 5})

integral of cot(4t)sqrt(1-sin^2(4t))

\int cot (4 t) 1 - sin^{2} (4 t) d t

integral of (5x^2-5x+14)/((x-2)(x^2+4))

\int \frac{5 x ^{2} - 5 x + 14}{( x - 2 ) ( x ^{2} + 4 )} d x

limit as x approaches-3 of x/(x^2-9)

x \to - 3 lim (\frac{x}{x ^{2} - 9})

Frequently Asked Questions (FAQ)

What is the derivative of e^{4/x} ?
The derivative of e^{4/x} is -(4e^{4/x})/(x^2)
What is the first derivative of e^{4/x} ?
The first derivative of e^{4/x} is -(4e^{4/x})/(x^2)