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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

e^{x} e^{l n (x)}

e^{- 3.43}

x^{- 4}

e^{- λ x}

(a^{2} b^{2} c) (a b^{3}) (a^{2} b c^{2})

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