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Popular >

derivative of e^{x/(x-4)}

Solution

derivative of

e^{\frac{x}{x - 4}}

Solution

- \frac{4 e ^{\frac{x}{x - 4}}}{( x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (e^{\frac{x}{x - 4}})

Apply the chain rule:

e^{\frac{x}{x - 4}} \frac{d}{d x} (\frac{x}{x - 4})

= e^{\frac{x}{x - 4}} \frac{d}{d x} (\frac{x}{x - 4})

\frac{d}{d x} (\frac{x}{x - 4}) = - \frac{4}{( x - 4 ) ^{2}}

= e^{\frac{x}{x - 4}} (- \frac{4}{( x - 4 ) ^{2}})

Simplify

e^{\frac{x}{x - 4}} (- \frac{4}{( x - 4 ) ^{2}}) : - \frac{4 e ^{\frac{x}{x - 4}}}{( x - 4 ) ^{2}}

= - \frac{4 e ^{\frac{x}{x - 4}}}{( x - 4 ) ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of e^{x/(x-4)} ?
The derivative of e^{x/(x-4)} is -(4e^{x/(x-4)})/((x-4)^2)
What is the first derivative of e^{x/(x-4)} ?
The first derivative of e^{x/(x-4)} is -(4e^{x/(x-4)})/((x-4)^2)