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

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

00:40

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

00:38

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Differentiate.

$ f…

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Derivatives Find and simpl…

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

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