MTH 161 Lecture Notes - Lecture 11: Product Rule, Quotient Rule

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6 Apr 2017
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2. 4 the product and quotient rules notes: sterling. Provide a generalization to each of the key terms listed in this section. If the following occurs: then the following would occur: y = f (x) g (x) = f (x) g (x) y = f (x) g (x) + f (x) g (x) What is the general product rule? d dx. [f (x) g (x)] = [f (x) g (x)] = f (x) g (x) + f (x) g (x) What is the product rule in leibniz" notation? d (uv) dx du dx (v) + u(cid:18) dv dx(cid:19) = u v + uv . Proof d dx [f (x) g (x)] = limh 0h f (x+h)g(x+h) f (x)g(x) h i h i. = limh 0h f (x+h)g(x+h) f (x+h)g(x) f (x)g(x)+f (x+h)g(x) i i. = limh 0h f (x+h)[g(x+h) g(x)]+g(x)[f (x+h) f (x)] h h.

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