What is the derivative of e^{x/((x-1)}) ?

The derivative of e^{x/((x-1)}) is -(e^{x/(x-1)})/((x-1)^2)

What is the first derivative of e^{x/((x-1)}) ?

The first derivative of e^{x/((x-1)}) is -(e^{x/(x-1)})/((x-1)^2)

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\frac{d}{d x} (e^{\frac{x}{( x - 1 )}})

- \frac{e ^{\frac{x}{x - 1}}}{( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (e^{\frac{x}{( x - 1 )}})

Apply the chain rule:

e^{\frac{x}{x - 1}} \frac{d}{d x} (\frac{x}{x - 1})

= e^{\frac{x}{x - 1}} \frac{d}{d x} (\frac{x}{x - 1})

\frac{d}{d x} (\frac{x}{x - 1}) = - \frac{1}{( x - 1 ) ^{2}}

= e^{\frac{x}{x - 1}} (- \frac{1}{( x - 1 ) ^{2}})

Simplify

e^{\frac{x}{x - 1}} (- \frac{1}{( x - 1 ) ^{2}}) : - \frac{e ^{\frac{x}{x - 1}}}{( x - 1 ) ^{2}}

= - \frac{e ^{\frac{x}{x - 1}}}{( x - 1 ) ^{2}}

\frac{5}{x + 6}

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

θ \to 0 lim (2 sec (θ))

(0, - 1), (6, 1)

x \to 0 - lim (\frac{x ^{3} + 3}{x})

What is the derivative of e^{x/((x-1)}) ?
The derivative of e^{x/((x-1)}) is -(e^{x/(x-1)})/((x-1)^2)
What is the first derivative of e^{x/((x-1)}) ?
The first derivative of e^{x/((x-1)}) is -(e^{x/(x-1)})/((x-1)^2)