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For what values of $ x $ does the graph of $ f $ have a horizontal tangent?$ f(x) = e^x \cos x $

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00:58

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

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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01:44

Locations of horizontal ta…

Hey, it's Claire so immune right here. So we're going to look for values of X. We're gonna start with the derivative. It has to be equal to zero. Since the graph of F has a horizontal attention, you have our original function, which is F of X is equal to eat. The X Times CO sign When we derive this, we're gonna eat. Use a product rule. We end up getting co sign terms each X plus e to X terms Negative sign This makes it equal to co sign next term's Eat the eggs, My nest each the X sign We're gonna take out E to the X We get go sign minus sign We make this equal to zero I mean, we end up getting co sign equals sign so X is equal to pi for plus Kate over Cape I. This is because you were using the reference of the unit circle

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