What is the derivative of e^{-ln(x}) ?

The derivative of e^{-ln(x}) is -1/(x^2)

What is the first derivative of e^{-ln(x}) ?

The first derivative of e^{-ln(x}) is -1/(x^2)

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\frac{d}{d x} (e^{- l n (x)})

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

Solution steps

\frac{d}{d x} (e^{- l n (x)})

Apply the chain rule:

e^{- l n (x)} \frac{d}{d x} (- ln (x))

= e^{- l n (x)} \frac{d}{d x} (- ln (x))

\frac{d}{d x} (- ln (x)) = - \frac{1}{x}

= e^{- l n (x)} (- \frac{1}{x})

Simplify

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

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

\int_{- 1}^{3} (x^{3} + 2 x - 5) d x

x \to 4 lim (x - 5)

\int - 2 x^{4} d x

y = x^{2} - 2 x, y = - x^{2} + 6 x

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

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