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Use the method of Exercise 55 to compute $ Q'(0). $ where
$ Q(x) = \frac {1 + x + x^2 + xe^x }{1 - x + x ^2 - xe^x} $
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01:49
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 2
The Product and Quotient Rules
Derivatives
Differentiation
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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In Exercises $55-60,$ veri…
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Hey, it's Claire is suing you right here. So we're gonna use the method of exercise 55 to get que the derivative of Q of zero and cue of accessible to warn. Plus acts plus x square plus X e x all over one minus next, plus X square minus X e to the X. So for EPA backs, we got one plus thanks. Bless Square plus X B to the X, which is the numerator. So when we derive this, we get zero plus one plus two x plus x Eat the X bless one times e to the X for G of X. You make this equal to the denominator, which is one minus x less X square minus x Eat the X. The derivative is equal to zero minus one less to x minus X e to the X minus one times E to the X. That's zero. It comes one, and the derivative of F of zero equals two. Fergie of zero. It's one, and the derivative of G 00 is too. So the derivative of F, divided by G. 00 is equal to G turns the derivative of minus f times the derivative of G over G Square. Look that only at one times to burn us more in terms negative too. All over one square equals four.
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