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Find an equation of the tangent line to the curve at the given point.
$ y = e^x $ cos $ x, (0.1) $
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00:55
Frank Lin
00:54
Clarissa Noh
Calculus 1 / AB
Chapter 3
Differentiation Rules
Section 3
Derivatives of Trigonometric Functions
Derivatives
Differentiation
Missouri State University
Campbell University
Oregon State University
Harvey Mudd 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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Alright, here's a fun calculus problem. We have the function Y equals E. To the X. Cosine effects. And our goal is to find the tangent line at 01. So we're going to first find the derivative and the derivative is going to be based on product roll. So we're gonna do the derivative of the first function times the second and then we're going to add to it. The derivative of the second time's the first. Well the derivative of cosine is minus sign and then we multiply times E. To the X. Alright so I can clean this up a little bit. I get E. To the X. Times Cosine of X minus sine of X. Alright so let's go ahead and find why prime at zero. Why prime that zero would be E. To the zero. Cosine of 0- sign of zero. Well either that zero is just one. Cosine of zero is also one and sine of zero is zero. So we just get one. Alright so let's now do our tangent line. Alright so our tangent line is of the form Y equals Y. Of zero plus Y. Prime of zero times X minus zero. So let's figure out our parts why of zero is 1 and why primer zero is also one. So wow this comes out really nice. So our tangent line is just simply one plus X. Or if you like Ah y equals x plus one. Um Alright excellent. That was fun. Alright. Have a wonderful day
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