Calculus UNIT301 What's the product rule?

2806 days ago by MATH4R2013

#1) f(x)=x g(x)=x^2 show(diff(f(x),x)) show(diff(g(x),x)) show(diff(f(x)*g(x),x)) show(f(x)*diff(g(x),x)+g(x)*diff(f(x),x)) 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) f(x)=x^2 g(x)=sin(x) show(diff(f(x),x)) show(diff(g(x),x)) show(diff(f(x)*g(x),x)) show(f(x)*diff(g(x),x)+g(x)*diff(f(x),x)) p1=plot(f(x)*g(x),0,5,color='red') p2=plot(diff(f(x)*g(x),x),0,5,color='green') p1+p2 
       




#3) f(x)=x^3 g(x)=cos(x) show(diff(f(x),x)) show(diff(g(x),x)) show(diff(f(x)*g(x),x)) show(f(x)*diff(g(x),x)+g(x)*diff(f(x),x)) p1=plot(f(x)*g(x),0,5,color='red') p2=plot(diff(f(x)*g(x),x),0,5,color='green') p1+p2 
       




#4) f(x)=x^3 g(x)=exp(x) show(diff(f(x),x)) show(diff(g(x),x)) show(diff(f(x)*g(x),x)) show(f(x)*diff(g(x),x)+g(x)*diff(f(x),x)) p1=plot(f(x)*g(x),0,5,color='red') p2=plot(diff(f(x)*g(x),x),0,5,color='green') p1+p2 
       




#5) f(x)=e^x g(x)=cos(x) show(diff(f(x),x)) show(diff(g(x),x)) show(diff(f(x)*g(x),x)) show(f(x)*diff(g(x),x)+g(x)*diff(f(x),x)) p1=plot(f(x)*g(x),0,5,color='red') p2=plot(diff(f(x)*g(x),x),0,5,color='green') p1+p2 
       




#6) f(x)=e^x g(x)=sin(x) show(diff(f(x),x)) show(diff(g(x),x)) show(diff(f(x)*g(x),x)) show(f(x)*diff(g(x),x)+g(x)*diff(f(x),x)) p1=plot(f(x)*g(x),0,5,color='red') p2=plot(diff(f(x)*g(x),x),0,5,color='green') p1+p2