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Let $ P(x) = F(x)G(x) $ and $ Q(x) = F(x)/G(x), $ where $ F $ and $ G $ are the functions whose graphs are shown.(a) Find $ P'(2). $(b) Find $ Q'(7). $
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01:12
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 2
The Product and Quotient Rules
Derivatives
Differentiation
Campbell University
Oregon State University
Harvey Mudd College
University of Michigan - Ann Arbor
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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Explorer. So when you read here, so for part A, we're first on apply the product world when we get the derivative of, uh, times the derivative of G plus the derivative of half times the derivative of G. We plug in to for X. When we get the derivative of P up to is equal to zero times two plus three times 0.5, which becomes equal to three halves. Report be we're gonna applied the quotient bull. So we have y is equal to you over B. That means the derivative of Y is equal to three times the derivative of you. Minus you turns the derivative of B over the square. So cue the derivative of Q is equal to G of X owns the derivative of X miners of X times, the derivative of G of X, all over G of X Square. Re plug in seven for X, and we get one times 1/4 minus five times negative 2/3 over one square, which is equal to 43 over 12
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