Let f and g be the functions in the table below.


Let f and g be the functions in the table below.

xf(x) g(x) f'(x)g'(x)
1 3 2 4 6
2 1 3 5 7
32 1 79

a) If F(x)=f(f(x)),find F '(2).

b) If G(x)=g(g(x)),find G'(1).

Chain Rule

One way that functions can be defined is through composition. In this type of function, we feed one function into another, yielding an expression in one of the two forms: {eq}(f \circ g)(x) = f(g(x)) {/eq}. The derivative of such a function can be calculated using the Chain Rule, which states that {eq}(f \circ g)'(x) = f'(g(x)) g'(x) {/eq}.

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a) This first function is defined by composing f with itself. In order to find the derivative of this function at a point, then, we need to use the...

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Using the Chain Rule to Differentiate Complex Functions


Chapter 8 / Lesson 6

Learn how to differentiate complex functions using the chain rule. Review an explanation of the chain rule and how to use it to solve complex problems like functions without parentheses and trig functions.

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