MAT237Y1 Lecture : 3.2 derivatives.pdf

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It"s all that stu we did last week. Denoted f(cid:48)(x) (pronounced f prime of x), it"s simply f(cid:48)(x) = lim h 0 f(x + h) f(x) h and is called the derivative with respect to x. The domain of f(cid:48)(x) is all the x in the domain of f(x) and where the above limit exists. Example: find the derivative with respect to x of f(x) = 3x2 2. [3(x + h)2 2] [3x2 2] h. [3(x2 + 2xh + h2 2] 3x2 + 2. 3x2 + 6xh + 3h2 2 3x2 + 2 h h. 6xh + 3h2 h h(6x + 3h) h. Keep in mind that the derivative is a function, so you should be getting out something with x in it. Only when we want to know what the derivative is at a speci c point (like, say, x = 3) do we only get a number out.

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