Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Differentiate the function.$ z = \frac {A}{y^{10}} + Be^y $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Carson Merrill
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
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.
01:01
Differentiate the function…
01:08
02:42
Find the derivative of eac…
05:18
01:45
02:05
01:18
Differentiate.
$ y…
01:25
00:54
03:43
02:53
Differentiate.$f ( z )…
01:16
$ f…
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.
View More Answers From This Book
Find Another Textbook
01:40
Find each solution set. Then classify each equation as either a conditional …
03:17
For Exercises 103–107, assume that a linear equation models each situation.<…
01:43
Classify each statement as either true or false. The following sets are used…
04:45
04:54
01:44
01:17
01:36
01:37
01:26
Factor completely.$x^{2}-25$
