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If f(x) is a function, then (f∘)(x)=f(f(x)) is the composition of f with itself. This is called an iterated function, and the composition can be repeated many times. For example, (f∘f∘f)(x)=f(f(f(x))). Iterated functions are very useful in many areas, including finance (compound interest is a simple case) and the science (in weather forecasting, for example). For each function, use the Chain Rule to find the derivative.
If f(x)=x+√x, find ddx[(f∘f)(x)].
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Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
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