Gavin's Calc II Class Clarification: Aug 23

We probably want to know the rules for the "elementary" functions,

(xn)' = n xn-1 (sin(x))' = cos(x)

(cos(x))' = -sin(x) (tan(x))' = 1 / (cos2(x))

(ex)' = ex (ln(x))' = 1 / x

And those for the rules for differentiation of combinations of functions:

	Product Rule	(u(x) v(x))' = u'(x) v(x) + u(x) v'(x)
		((first)(second))' = (derivative of first)(second) + (first)(derivative of second)
		e.g., (x ln(x))' = (1)(ln(x) + (x)(1 / x)
	Quotient Rule	(u(x) / v(x))' = (u'(x) v(x) - u(x) v'(x)) / v2(x)
		(top / bottom)' = ((derivative of top)(bottom) - (top)(derivative of bottom)) / (bottom)2
		e.g., (x / ex)' = ((1)(ex) - (x)(ex)) / (ex)2
	Chain Rule	(u(v(x)))' = u'(v(x)) v'(x)
		(outer(inner(x)))' = (derivative of outer with inner plugged in)(derivative of inner)
		e.g., (cos(ln(x)))' = -sin(ln(x)) (1 / x)

We'll see this in class shortly.