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If $ g(x) = xf(x), $ where $ f(3) = 4 $ and $ f'(3) = - 2. $ find an equation of the tangent line to the graph of $ g $ at the point where $ x = 3. $
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00:57
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 2
The Product and Quotient Rules
Derivatives
Differentiation
Campbell University
University of Nottingham
Idaho State University
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.
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Hey, it's clear. So when you read here, so our first gonna use the product roll to find the derivative of G. So it g of X is equal to x times athletics. So the derivative of G it's gonna be equal to that of acts plus x times the derivative of Then we're gonna find too derivative after we plug in three Fergie, the derivative of G of three. And we're gonna use our given values three times the derivative of us of three, which is equal to four plus three times negative too, which is equal to negative, too. So this is gonna be the Slope M of detention line to G of X at X equals three. And we need to find the value for G up three. And we get well, so our line equation why minus y one equals M on X minus X one, and all we do is just plug in, make it why is equal to negative two x plus 18
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