Calculus UNIT302 What's the Quotient Rule?

2808 days ago by MATH4R2013

#1) Don't forget the Product Rule! f(x)=x^2+1 g(x)=x^3+3 show(diff(f(x),x)) show(diff(g(x),x)) show(diff(f(x)*g(x),x).expand()) show((f(x)*diff(g(x),x)+g(x)*diff(f(x),x)).expand()) p1=plot(f(x)*g(x),0,5,color='red') p2=plot(diff(f(x)*g(x),x),0,5,color='green') p1+p2 
       




#2) Now try the Qutient Rule! f(x)=x^2-1 g(x)=x^2+1 show(diff(f(x),x)) show(diff(g(x),x)) show(diff(f(x)/g(x),x).simplify_rational()) p1=plot(f(x)/g(x),-5,5,color='red') p2=plot(diff(f(x)/g(x),x),-5,5,color='green') p1+p2 
       



#3) find the tangent line to f(x)=x+2/x when x=1 f(x)=x+2/x g(x)=diff(f(x),x) show(f(x)) show(g(x)) show(f(1)) show(g(1)) p1=plot(f(x),0.5,3,color='red') p2=plot(g(1)*(x-1)+f(1),0.5,3,color='green') (p1+p2).show(aspect_ratio=1)