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If $ f(x) = e^x g(x), $ where $ g(0) = 2 $ and $ g'(0) = 5, $ find $ f'(0). $
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00:39
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 2
The Product and Quotient Rules
Derivatives
Differentiation
Oregon State University
Baylor University
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.
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Hey, it's Claire. So in your rain here. So we're first when he used a product rule to find the formula for the derivative of F in terms of G. So we have the derivative of this equal to the derivative of E to the X turns g of X, less eat the eggs, terms the derivative of G X, and this is equal to eat the x times g to the ex less e to the X times, the derivative of G events. And then we're gonna just plug in what we know. So we get thanks the derivative of f of zero, which is equal to e to the zero times two less e to the zero times five. There's just becomes, too. This just becomes by we act these two together and get seven.
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