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(a) Find an equation of the tangent line to the curve $ y = 3x + 6 $ cos $ x $ at the point $ (\pi/3, \pi + 3). $(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.
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00:53
Frank Lin
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 3
Derivatives of Trigonometric Functions
Derivatives
Differentiation
Campbell University
Harvey Mudd College
University of Nottingham
Boston College
Lectures
04:40
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
44:57
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
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$\begin{array}{l}{\text { …
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(a) Find an equation of th…
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a. Find an equation of the…
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Equations of tangent lines…
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(a) Use a graphing utility…
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it's clear. So when you right here. So I first gonna get the derivative. Once we get the derivative, we get three minus six sign we're gonna evaluate for X is equal to tie over three. We have three minus six on square root of three. I want it by two. We're gonna put it Plug in the point on the slope when we get one is minus. Hi. Plus three is equal to three minus three square root of three. I'm specs minus points. We get why is equal to pi. Plus three plus three minus three square root of three when x minus pi. Third part B. We're going to draw a graph, so we have thanks. And the graph looks roughly this and then our would draw our line.
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