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Popular >

derivative of e^{x/((x-6)})

Solution

\frac{d}{d x} (e^{\frac{x}{( x - 6 )}})

Solution

- \frac{6 e ^{\frac{x}{x - 6}}}{( x - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (e^{\frac{x}{( x - 6 )}})

Apply the chain rule:

e^{\frac{x}{x - 6}} \frac{d}{d x} (\frac{x}{x - 6})

= e^{\frac{x}{x - 6}} \frac{d}{d x} (\frac{x}{x - 6})

\frac{d}{d x} (\frac{x}{x - 6}) = - \frac{6}{( x - 6 ) ^{2}}

= e^{\frac{x}{x - 6}} (- \frac{6}{( x - 6 ) ^{2}})

Simplify

e^{\frac{x}{x - 6}} (- \frac{6}{( x - 6 ) ^{2}}) : - \frac{6 e ^{\frac{x}{x - 6}}}{( x - 6 ) ^{2}}

= - \frac{6 e ^{\frac{x}{x - 6}}}{( x - 6 ) ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of e^{x/((x-6)}) ?
The derivative of e^{x/((x-6)}) is -(6e^{x/(x-6)})/((x-6)^2)
What is the first derivative of e^{x/((x-6)}) ?
The first derivative of e^{x/((x-6)}) is -(6e^{x/(x-6)})/((x-6)^2)