MTH 252 Lecture Notes - Lecture 5: General Idea
13 Sep 2016
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Review of single variable differentiation (a,f(a)) tangent line in blue. The tangent line approximates the function such that: but this is an approximation, and we want a general equation for any point. Recall that the derivative for any one dimensional function is as follows: This is similar to what we use for 2-d and 3-d a. Tangent planes are used instead of tangent lines in 2-d and 3-d. The algebra of derivatives: or set x = 2, so that you will intersect this with the plane x=2. Definition: the partial derivatives of f at (a,b) are defined as: Then take the derivative as normal in 1 dimension: can be rewritten as. Then take the derivative as normal in 1 dimension: Definition: we define the functions and to be and wherever these limits exist. In finding from , you treat y as a constant and differentiate with respect to x.
