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Suppose y=x^2. So dy/dx=2x. If we let x=t then we have a vector valued function r(t)=<t,t^2>. Hence r'(t)=<1,2t>. As can be seen we will not have the gradient after we take the modules of r'(t). Where am I going wrong. Also suppose I went on plotting r'(t) I will get a vertical line which is pretty useless and not as informative as dy/dx=2x. What's happening?