![]() We offer tutoring programs for students in K-12, AP classes, and college. SchoolTutoring Academy is the premier educational services company for K-12 and college students. Differentiation: Solve exercises 38 and 40 of E&P section 3.1 pp 113. ![]() Interested in calculus tutoring services? Learn more about how we are assisting thousands of students each academic year. Then f(y)=sin(y) and g(x)=2x, so sin(2x) can be written as f(g(x)). It can be thought of as a chain, in that first we take the derivative of the outer equation and then move steadily inward. Homework Equations (g o f) (x) g(f (x)) f(x) MVT The Attempt at a Solution /B I know that the open interval (a n, x) is a subset of J. Use the mean value theorem to prove the chain rule. The function f takes I to J, and the function g take J to R. So since j(x)=g(h(x)), we can rewrite this as f'(g(h(x)))*(g(h(x)))’, or f'(g(h(x)))g'(h(x))h'(x). Homework Statement I and J are open subsets of the real line. Think of it instead as f(j(x)) where j(x) = g(h(x)), and as we know the derivative of f(j(x)) is f'(j(x))j'(x). The Chain Rule One of the challenges of differentiating a composite function is that it often cannot be written in an alternate algebraic form. Then it can be broken thought of as doing the chain rule multiple times. If the equation is more complicated, such as ![]() Suppose we have an equation written as f(g(x)). In reality, although these may look tricky, they are actually fairly straightforward. ![]() Occasionally, you will have what are called composite functions that is, functions that are composed of multiple functions and thus cannot be differentiated easily.
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