What is the derivative of e^{-x/y} ?

The derivative of e^{-x/y} is -(e^{-x/y}(y-x\frac{dy)/(dx))}{y^2}

What is the first derivative of e^{-x/y} ?

The first derivative of e^{-x/y} is -(e^{-x/y}(y-x\frac{dy)/(dx))}{y^2}

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Popular >

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

- \frac{e ^{- \frac{x}{y}} ( y - x \frac{d y}{d x} )}{y ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (\frac{4}{3} p i x^{3})

3 x^{2}, at x = 4

x \to 5 lim (x)

t \to + 0 lim (\frac{8}{t} - \frac{8}{t ^{2} + t})

\int 6 x d x

What is the derivative of e^{-x/y} ?
The derivative of e^{-x/y} is -(e^{-x/y}(y-x\frac{dy)/(dx))}{y^2}
What is the first derivative of e^{-x/y} ?
The first derivative of e^{-x/y} is -(e^{-x/y}(y-x\frac{dy)/(dx))}{y^2}