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Numerade Educator

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Problem 28 Easy Difficulty

Find the derivative of the function.
$ f(z) = e^{z/(z - 1)} $

Answer

$\frac{-e^{\frac{z}{z-1}}}{[z-1]^{2}}$

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Video Transcript

Let's find the derivative of F of Z equals e to the T oversee minus one. And in general, the derivative of E to a function is each of that function times the derivative of that function. So the derivative here should be e to the Z over Z minus one times the derivative of the over Z minus one. So to find the derivative of the over Z minus one, we can use the quotient rule. So we have the bottom Z minus one times the derivative of the top one, minus the top Z times. The derivative of the bottom, the derivative of Z minus one would be one over the bottom squared so over Z minus one squared. Now we can simplify that. So simplifying the numerator Z minus one minus Z would just be negative one so altogether than are derivative is negative one times e to the C over Z minus one over C minus one quantity squared