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(a) Find an equation of the tangent line to the curve $ y = 2x $ sin $ x $ at the point $ (\pi/2, \pi). $(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.

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(a) $$y-\pi=2\left(x-\frac{\pi}{2}\right), \text { or } y=2 x$$(b)

00:50

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

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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it's clear, so enumerated here. So for part A, we have why is equal to two X sign about? We used the product Fool. I get why the derivative is equal to the derivative of two X I'm sign plus two x who owns the derivative of sign This gives us to sign plus two x co sign Plug in pi over too. Your ex first slope You get two. So using the point slope formula. Yet why minus pi is equal to two times x minus pi over too. Which gives us Why is he called to two sets Next? We're going to go ahead and illustrate it. We have our X and y our original graph. Look something like this. Why? To pine Murray tangents.

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