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Use the Chain Rule lo show that if $ \theta $ is measured in degrees, then$ \frac {d}{d \theta} (\sin \theta) = \frac {\pi}{180} \cos \pi $(This gives one reason for the convention that radian measure is always used when dealing with trigonometric functions in calculus: the differentiation formulas would not be as simple if we used degree measure.)

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00:37

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 4

The Chain Rule

Derivatives

Differentiation

Missouri State University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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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Use the Chain Rule to show…

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Use the Chain Rule and the…

The differentiation formul…

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Use the Chain Rule to find…

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Use the rules of different…

Okay, so we typically working radiance and calculus. But what if we decided to work in degrees? We know that fate a radiance is equal to pi over 1 80 tons x degrees. So if we had the function y equals sine data, we could think of it as why equals the sign of pi over 1 80 times X. Now, suppose we wanted to find its derivative. We would need to use the chain rule. The derivative of the outside would be co sign so we would have co sign of pi over 1 80 times X times the derivative of the inside and the derivative of the inside would be pi over 1 80 Now, if we went back and placed the pi over 1 80 in the beginning of the expression and then if we substituted Fada back in here for pi over 1 80 times X, we would have pi over 1 80 times a co sign of data. So this is much more complicated as a derivative than if we just use radiance

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