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Popular >

derivative of e^{x/(x-3})

Solution

\frac{d}{d x} (e^{\frac{x}{x - 3}})

Solution

- \frac{3 e ^{\frac{x}{x - 3}}}{( x - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (e^{\frac{x}{x - 3}})

Apply the chain rule:

e^{\frac{x}{x - 3}} \frac{d}{d x} (\frac{x}{x - 3})

= e^{\frac{x}{x - 3}} \frac{d}{d x} (\frac{x}{x - 3})

\frac{d}{d x} (\frac{x}{x - 3}) = - \frac{3}{( x - 3 ) ^{2}}

= e^{\frac{x}{x - 3}} (- \frac{3}{( x - 3 ) ^{2}})

Simplify

e^{\frac{x}{x - 3}} (- \frac{3}{( x - 3 ) ^{2}}) : - \frac{3 e ^{\frac{x}{x - 3}}}{( x - 3 ) ^{2}}

= - \frac{3 e ^{\frac{x}{x - 3}}}{( x - 3 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^{x/(x-3}) ?
The derivative of e^{x/(x-3}) is -(3e^{x/(x-3)})/((x-3)^2)
What is the first derivative of e^{x/(x-3}) ?
The first derivative of e^{x/(x-3}) is -(3e^{x/(x-3)})/((x-3)^2)