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

The derivative of e^{x/y} is (e^{x/y})/y

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

The first derivative of e^{x/y} is (e^{x/y})/y

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derivative of

e^{\frac{x}{y}}

\frac{e ^{\frac{x}{y}}}{y}

Solution steps

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

Treat

y

as a constant

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{1}{y}

= e^{\frac{x}{y}} \frac{1}{y}

Simplify

e^{\frac{x}{y}} \frac{1}{y} : \frac{e ^{\frac{x}{y}}}{y}

= \frac{e ^{\frac{x}{y}}}{y}

3 (e^{x} cos (x) - e^{x} sin (x))

x \to 0 lim (\frac{6 x + 4 - 2}{x})

5 e^{- 6 x}

\int \frac{( x ^{4} + 1 )}{x ^{3} + 2 x ^{2} + x} d x

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

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