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If $ g(x) + x \sin g(x) = x^2, $ find $ g'(0). $

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01:25

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Missouri State University

Oregon State 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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if this problem were given any question on and years to find their function. G when exes. Zira, let's first find the value of that function when x zero Solis for G zero. So we're gonna play zero in terms of eggs. So we have g 00 was zero times sine GOP zero as people to zero this term is zero. So from this BC, that G o P zero is zero. And let's tag narrative All think of the question. You have G primal X plus breaking news for a cool for a second term of left hand side, we have a sign your ex waas um X times consign g o eggs times deeper X is equal to x. No less plays you're in. You have g p zero plus sign G off zero plus zero times. Co sign g +00 times zero is zero. This storm is zero. We have signed you up zero but be known at jobs series itself, his ears off signing zero sign of serious. You're so from this we see that GI problems here put there a physical zero. So Jeep ERM of zero is the U

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