MATA32H3 Lecture Notes - Lecture 1: Inverse Hyperbolic Function, Quotient Rule, Product Rule

• School: UTSC
• Department: Mathematics
• Course: MATA32H3
• Professor: Raymond Grinnell

Document Summary

Derivatives dx [xn] = nxn 1 d dx [c] d dx [x] = 1 d x2i = 2 dx h 1 x3 dx [ x] = = sech 2x d d dx [ex] dx [bx] d dx [ln x] d dx [logb x] d dx [sinh x] d dx [cosh x] d dx [tanh x] d dx [arcsinh x] = d dx [arctanh x] = 1 x2 d dx [sin x] d dx [cos x] d dx [tan x] d dx [sec x] d dx [arcsin x] = d dx [arctan x] = Product rule: d dx [f (x)g(x)] = f (x)g(x) + f (x)g (x) Quotient rule: d dx (cid:20) f (x) g(x)(cid:21) = g(x)f (x) f (x)g (x) g(x)2. [f (g(x))] = f (g(x))g (x) or dy dx dy du du dx. = nf (x)n 1f (x) d dx (cid:20) 1 g(x)(cid:21) [ln|f (x)|] = f (x) f (x) d dx hef (x)i.