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Popular >

derivative of e^{x/y}

Solution

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

Solution

\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}}

Multiply fractions:

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

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

Popular Examples

simplify 12e^{-0}simplify

12 e^{- 0}

simplify (sqrt(k+1))/(sqrt(k))simplify

\frac{k + 1}{k}

simplify sqrt(6-x)sqrt(1+1/(4(6-x)))simplify

6 - x 1 + \frac{1}{4 ( 6 - x )}

simplify e^{-3}(3-2)simplify

e^{- 3} (3 - 2)

simplify e^{-x}(e^x+e^{-x})simplify

e^{- x} (e^{x} + e^{- x})

Frequently Asked Questions (FAQ)

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}