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Popular >

derivative of e^{((-k/x)})

Solution

\frac{d}{d x} (e^{(\frac{- k}{x})})

Solution

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

Solution steps

\frac{d}{d x} (e^{(\frac{- k}{x})})

Simplify

e^{(\frac{- k}{x})} : e^{- \frac{k}{x}}

= \frac{d}{d x} (e^{- \frac{k}{x}})

Apply the chain rule:

e^{- \frac{k}{x}} \frac{d}{d x} (- \frac{k}{x})

= e^{- \frac{k}{x}} \frac{d}{d x} (- \frac{k}{x})

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Popular Examples

derivative of 2(sin(x^2)+2x^2cos(x^2))derivative of

2 (sin (x^{2}) + 2 x^{2} cos (x^{2}))

tangent of f(x)= 1/(sqrt(3x)),\at x=9 tangent of

f (x) = \frac{1}{3 x}, at x = 9

limit as x approaches-7 of (7-|x|)/(7+x)

x \to - 7 lim (\frac{7 - ∣ x ∣}{7 + x})

integral from 1 to 5 of (ln(y))/(xy)

\int_{1}^{5} \frac{ln ( y )}{x y} d y

(e^{- 4 x})^{^{'}}

Frequently Asked Questions (FAQ)

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