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Suppose that $ f(5) = 1, f' (5) = 6, g(5) = -3, $ and $ g'(5) = 2. $ Find the following values.(a) $ (fg)' (5) $
(b) $ (f/g)' (5) $
(c) $ (g/f)' (5) $
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02:00
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 2
The Product and Quotient Rules
Derivatives
Differentiation
Campbell University
University of Michigan - Ann Arbor
Idaho State University
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.
04:33
Suppose that $f(5)=1, f^{\…
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Let $f(x)=2 x-5$ and $g(x)…
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Let $f(x)=3 x+5$ and $g(x)…
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Given $f(x)=5 x-1$ and $g(…
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Given $f(x)=6 x+5$ and $g(…
00:51
feats. Clearasil on rain here. So, for part A, we're gonna use the product rule. Let me get F G. Derivative five is equal to derivative of F five GF five less five derivative of G of five. You plug it in and you get six times negative. Three plus one times two, which is equal to negative 16. We have part being f departed by G. The derivative of five is equal to the drill bit it, uh, the five g of five minus F five. The derivative of chief of Fly all over G of five square and you get six times negative. Three minus one times two over a negative three square, giving us negative. 20 over nine For part C, you have Jeanne divided by s the derivative five, which is equal to the derivative of G of five. Yes, a five minus g of five. The derivative of F of five all over five square. This is equal to two time one minus negative. Three. I'm six over one square, which is equal to 20
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