We have f(x) = 1/sin x. Here, u(x) equals one and v(x) equals sin x. Thus, u'(x) equals 0 and v'(x) equals cos x. We obtain f'(x) = [v(x) u'(x) â u(x) v'(x)] using the quotient rule. /[v(x)] 2 equals [sin x (0) â 1 (cos x)] /cos2 x equals -cos x/ cos2 x equals -1/cos x equals -sec x
Calculating the products of more than two functions is really rather straightforward. Consider the three function product rule, for instance. To begin, we do not consider it a product of three functions, but rather the product rule of two functions (f,g) and (h), on which we may then apply the two function product rule. This results in,
