MAT 212 Chapter Notes - Chapter 6: Riemann Sum, Asymptote, Partial Function
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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 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 h. = f (x) limh 0h g(x+h) g(x) h i + g (x) limh 0h f (x+h) f (x) h i. = f (x) g (x) + g (x) f (x)
