The key to studying the chain rule, as well as any of the differentiation rules, is to practice with it as much as possible. Mastering the chain rule is incredibly important for success on the AP Calculus exam. You will find that chain rule problems often involve sin, cos, and tangent, as we often use trigonometric along with other functions. We can use the chain rule multiple times in a row as well. We can also use the chain rule in combination with the other rules.Īgain, we can use chain rule in combination with other rules. (This can be reduced to cos(2x) if you know your trig identities.) Many students get confused between when to use the chain rule (when you have a function of a function), and when to use the product rule (when you have a function multiplied by a function). This one is thrown in purposely, even though it is not a chain rule problem. Solutions and Explanations to Example Problems You do not need a calculator to answer any of these questions. Here is a list of example problems of varying difficulties. This is going to be a rule which is very important to practice with over and over again. The problem that many students have trouble with is trying to figure out which parts of the function are within other functions (i.e., in the above example, which part if g(x) and which part is h(x). Implementing the chain rule is usually not difficult. You can find a list of common derivatives as well as explanations of the other derivative rules in our review of derivative rules. The derivative of h(x) can be solved with the power rule, and the derivative of g(x) is a common derivative. These Calculus Worksheets will produce problems that involve using the chain rule to differentiate functions. The chain rule allows us to take the derivative of the entire thing. we can find the derivative of each of these functions individually. You can think of f(x) = g(h(x)), where h(x) = x 2 and g(x) = sin(x). Our function f(x) is made up of two smaller functions. The chain rule is used when we have a function which is of the form f(x) = g(h(x)). What is the chain rule and when do we use it? The chain rule is one of the most important rules in this list because many function cans be thought of as functions of functions (of functions of functions). The last thing we want to get caught up in on the exam is forgetting one of our derivative taking methods, such as the chain rule. We should know how to use all the most common methods for taking the derive well enough that we don’t have to think about it on the exam itself. For the AP Calculus exam, whether it’s Calculus AB or Calculus BC, being completely fluent in taking the derivative of almost any function is imperative. Practice Solutions c3.4practicesolutions.pdf Download File Corrective Assignment c3.4ca.pdf Download File Below is a walkthrough for the test prep questions.
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