For example, we had the special rule for squares of functions:

d/dx[f

^{2}(x)] = 2 f(x) f '(x)

This means that any time there is a formula squared and you need to take its derivative, you can apply this rule.

(2x+3)

^{2}corresponds to the function f(x)=2x+3 being squared. So since f '(x) = 2:

d/dx[(2x+3)

^{2}] = 2 (2x+3) (2) = 4(2x+3)

Similarly, (x

^{2}-4x+5)

^{2}corresponds to the function f(x) = x

^{2}-4x+5 being squared, and f '(x)=2x-4

d/dx[(x

^{2}-4x+5)

^{2}] = 2 (x

^{2}-4x+5) (2x-4)

You need to be an expert at identifying the form of an expression in order to apply appropriate rules of differentiation, and next semester, rules of integration (anti-differentiation).

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