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Differentiate the function.$ y = x^{5/3} - x^{2/3} $
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00:27
Frank Lin
01:19
Clarissa Noh
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 1
Derivatives of Polynomials and Exponential Functions
Derivatives
Differentiation
Missouri State University
Harvey Mudd College
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.
Differentiate the function…
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Differentiate each functio…
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Differentiate.$$f(…
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Differentiate.$$f(x)=\…
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All right. So our goal is to find the derivative of X to the five thirds minus X to the two thirds. And let me just remind you that if we have any kind of power term where N could be a positive number, a negative number or even a fraction. Then the derivative by power rule goes like this will bring the end in front of the multiplier and then the power of X gets reduced by one. So this is what we're going to do to solve our derivative. So the derivative of why with respect to X, we're gonna bring that multiplier in front And then lower the exponent by one. Well we can do that. Well, I'll show it like this but I'll go ahead and then we'll kind of show the common denominator next time. So the next term is minus that two thirds goes in front and then we have to subtract one off our exponent. So we'll finally then clean that up. So we get five thirds X to them. We think of one as three thirds, then five thirds minus three thirds is two thirds. And for the last term 2/3 -3/3 will be -3. So there we have it. We have found our derivative using power roll. Alright, have a wonderful day
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