ENV100H1 Lecture 7: Derivatives Recap
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ENV100H1 Full Course Notes
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Soon we"re going to look into implicit di erentiation, which adds a new layer of di culty onto the subject. So, lets make sure we"re good with explicit derivatives (what we"ve been doing). Current rules: all with respect to (using) x as the variables, all other terms are constants. = f (x)g(x) + f (x)g (x: power rule. [ f (x: chain rule f (x)g(x) f (x)g (x) (g(x))2. With the exception of the chain rule, all of these apply only when the outermost interaction in the function being di erentiated relates to what they cover. The chain rule applies any time you have a function inside another, and the outside function is the outermost interaction. Technically it applies pretty much all the time, since sin(x) is a sine function with the function x inside, so we get which is the same as cos(x). cos(x) (x) = cos(x) (1) X 2 x x2 1 (15x 1)5 cos(e3x.
