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Differentiate the function.$ z = \frac {A}{y^{10}} + Be^y $

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00:33

Frank Lin

00:50

Clarissa Noh

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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.

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So for this problem, we're asked to differentiate. The function and the function were given is ah function of why the function is e. So it's Z equals, uh, a over 10 y or a over right to the 10th. So a over y 2/10 and then it's going to be plus B E to the y. So with differentiation, we know that we can take each portion of the some, um and then add those derivatives up separately. So Z Prime is going to equal first the derivative of this, plus the derivative. This the way we can write this, which would make it a lot easier for us, is a Y to the negative. 10th. That way, it's much easier to differentiate. We don't have to use the the quotient role, so we'll bring our negative 10 out in front a. Why. And then it's going to be now to the negative 11th because we subtract one. Explain it. Another way we could do this, though, would be to put this underneath y to the 11th, so it's in the similar form, and then lastly, what we'll do is add be we know each other, why it's derivative is just each of the Y on. We would use change role to differentiate the exponents, but we're differentiating with respect to why so it'll just stay like this. Now we have our final differentiated form of the function.

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