I think this practice is helpful to understand the meaning of dy/dx and how it comes about. This practice also transitions well as we move the students into related rates. The students then get a better understanding of how dt comes into the picture and the algebra behind it.
Douglas A. Dosky (c) 614-260-4699 email: firstname.lastname@example.org Thomas Worthington High School AP Calculus BC and AB Teacher ________________________________________ From: Lin McMullin [email@example.com] Sent: Monday, December 19, 2011 10:36 PM To: AP Calculus Cc: AP Calculus Subject: Re: [ap-calculus] dx/dx?
I've seen this done before. It serves to help kids and others to differentiate until you get to the variable, therefore they don't forget to differentiate y and get the dy/dx which kids and others sometimes do forget.
Lin McMullin 3520 Christopher Lane Richardson, Texas 75082
On Dec 19, 2011, at 15:04, "Beth Gallis" <firstname.lastname@example.org> wrote:
> When differentiating x^2+y^2=k implicitly, a colleague writes > > 2x* dx/dx + 2y* dy/dx =0. then 2x + 2y*dy/dx =0 since dx/dx =1. > > This seems like nonsense to me, since the derivative of x^2 with respect to x is just 2x - obviously x doesn't change with respect to x. Seems like a rote procedure so kids always put dsomething/dx. > > What do you all think?
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