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Find $ R'(0), $ where

$ R(x) = \frac {x - 3x^3 + 5x^5}{1 + 3x^3 + 6x^6 + 9x^9} $

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01:03

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

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.

02:50

Solve each equation. $…

01:04

Solve the equation.$$3…

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Solve the following equati…

00:50

00:40

Solve the polynomial equat…

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Solve the equations.$$…

02:20

01:08

Hey, it's Claire. So when you right here. So we're gonna make effort. X be equal to UPS minus three. X cube plus five X to the fifth. We're gonna make G of X one plus three X cube plus six x to the sick plus nine x to the ninth power. So are derivative D R. Over D X is equal to the derivative of of of axe ones G FX minus the X Times, the derivative of GI effects Wilbur G of X Square. When we plug in zero, we get the Durban. She is zero minus zero. Oh, we're G of zero square and this becomes equal to when we substituted one.

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