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Make a careful sketch of the graph of $ f $ and below it sketch the graph of $ f' $ in the same manner as in Exercises 4-11. Can you guess a formula for $ f'(x) $ from its graph?

$ f(x) = \sin x $

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03:02

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Missouri State University

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

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.

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in this problem. It is asked to make a careful sketch of the graph of F and below it. A sketch the graph F dash In the same manner as in exercises 4-11. Can you guess the formula for F--X from its craft? Great. So here we know this is a sign girl, right? By is equal to X. Is equal to sine X. So, we know about this side X. All right. So here the differentiation of uh cynics will be cause it's Okay. So this is also given by 19 minus theta or sign 90 plus X will be transformed into cost tita. Or you can see here I'm writing cause X. Because we are using ambulance cause X. Nd form X ray. So you're a real big X. Okay, so now we noticed that means the you can see the curve of Cossacks will start from here From 90 degree late 1990 plus 10 is given to us. Right? So in this way we will just project it in this way this this web form will start from here. Okay, remember this. So this will give me like this. Right? So that's gonna give me. Right, okay. So is it the same I'm getting here. 123. This is 12. This is 12. Okay. Two. Yeah. Mhm. Okay. Mhm. Mhm. Right, so here we have plotted the uh plotted to drive for cause eggs here. Right, so this is basically we can say that in this way we plot this formula. So this will be uh signed 90 plus X equals two Cossacks here. Right. One thing and we know the differentiation of cynics that is classics. Okay, So this is how we solve this problem, and same as before. The cycle will remain to to buy here, right? And then again, it starts from the same here, right? So from to find its again, starting the same thing. Okay, so this is how we have solved this problem. Thank you for watching.

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