10 SCREEN 12
20 PRINT "           Proof of the Quotient Rule"
30 PRINT "Prove: if f(x)=g(x)/h(x) then f'(x)=g'(x)h(x)-h'(x)g(x)/h(x)^2"
40 PRINT "f(x)=g(x)h(x)^-1"
45 PRINT "Using the product rule and the chain rule"
50 PRINT "f'(x)=g'(x)h(x)^-1+g(x)[-1h(x)^-2]h'(x)=g'(x)h(x)-g(x)h'(x)/h(x)^2"
60 PRINT "Example: f(x)=tan(x)=sin(x)/cos(x)"
70 PRINT "f'(x)=sin(x)'cos(x)-cos(x)'sin(x)/cos^2(x)=cos^2(x)+sin^2(x)/cos^2(x)"
80 PRINT "=1/cos^2(x)=sec^2(x)"
90 SYSTEM