Calculus UNIT301 What's the product rule? -- Sage

#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

 $\newcommand{\Bold}[1]{\mathbf{#1}}1$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}2 \, x$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2}$

#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

 $\newcommand{\Bold}[1]{\mathbf{#1}}2 \, x$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} \cos\left(x\right) + 2 \, x \sin\left(x\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} \cos\left(x\right) + 2 \, x \sin\left(x\right)$

#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

 $\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(x\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}-x^{3} \sin\left(x\right) + 3 \, x^{2} \cos\left(x\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}-x^{3} \sin\left(x\right) + 3 \, x^{2} \cos\left(x\right)$

#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

 $\newcommand{\Bold}[1]{\mathbf{#1}}3 \, x^{2}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}e^{x}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}x^{3} e^{x} + 3 \, x^{2} e^{x}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}x^{3} e^{x} + 3 \, x^{2} e^{x}$

#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

 $\newcommand{\Bold}[1]{\mathbf{#1}}e^{x}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}-\sin\left(x\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right) e^{x} - e^{x} \sin\left(x\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right) e^{x} - e^{x} \sin\left(x\right)$

#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

 $\newcommand{\Bold}[1]{\mathbf{#1}}e^{x}$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right) e^{x} + e^{x} \sin\left(x\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(x\right) e^{x} + e^{x} \sin\left(x\right)$

Calculus UNIT301 What's the product rule?

2806 days ago by MATH4R2013