The chain rule can be used to derive some well-known differentiation rules. For example, the quotient rule is a consequence of the chain rule and the product rule.
Once this is done, you may ask about the derivative of ? The answer can be found using similar trigonometric identities, but the calculations are not as easy as before.
How to apply the chain rule. ... Example 2. What is the derivative of y = sin 3 x? Solution. This is the 3rd power of sin x.
Cheat Sheets & Tables Algebra, Trigonometry and Calculus cheat sheets and a variety of tables. Class Notes Each class has notes available. Most of the classes have ...
Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with ...
Chain Rule. The chain rule allows us to differentiate a function that contains another function. What does that mean? Let's start with an example:
USING THE CHAIN RULE The following problems require the use of the chain rule. The chain rule is a rule for differentiating compositions of functions.
The method is called the "chain rule" because it can be applied sequentially to as many functions as are nested inside one another. For example, if f is a function of ...
REFERENCES: Anton, H. "The Chain Rule" and "Proof of the Chain Rule." §3.5 and AIII in Calculus with Analytic Geometry, 2nd ed. New York: Wiley, pp. 165-171 and A44 ...
#10: Derivatives and Rates of Change. #11: Chain Rule. #12: Super Related Rates