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Math and Science => Technology & Calculator Open Topic
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Flofloflo

Member

Joined: 07 Nov 2007
Posts: 120

 Posted: 13 Sep 2009 05:30:45 am    Post subject: hello, can somebody help me with implicit differentiation? basically, this is my problem: y=x^(1/n) x=y^n d/dx(x) = d/dx(y^n) d/dx(y^n) = ny^(n-1) * dy/dx I don't understand that last step. Why do I have to multiply by dy/dx? I am quite unfamiliar with Leibniz notation. My calculus book explains the last step with 'Recalling that y is a function of x, we may evaluate the left-hand side by the chain rule (or the power of a function rule) to get:' and the the thing I wrote down earlier. Of course, I know they are using the power or chain rule, but why the multiplication? I am bad with Leibniz notation (I will of course try to improve this, but my math study only just started). I interpret the last formula as: d/dx(y^n) = dx/dy * dy/dx. Does that make sense? Help would be appreciated. -florisLast edited by Guest on 13 Sep 2009 06:34:39 am; edited 1 time in total
thornahawk
μολών λαβέ

Active Member

Joined: 27 Mar 2005
Posts: 569

 Posted: 13 Sep 2009 10:14:12 am    Post subject: Remember that y in there is in fact a function y(x). With the chain rule, how do you differentiate y(x)n? thornahawk
Flofloflo

Member

Joined: 07 Nov 2007
Posts: 120

 Posted: 13 Sep 2009 11:57:34 am    Post subject: Simply n * y(x)^(n-1) What they do is multiply it by dy/dx. That doesn't make sense to me.... O_o
thornahawk
μολών λαβέ

Active Member

Joined: 27 Mar 2005
Posts: 569

 Posted: 13 Sep 2009 07:02:36 pm    Post subject: See, n*yn-1 is the derivative with respect to y.That doesn't take into account that y is a function of x. That's why I was alluding to the chain rule... after taking the derivative of yn with respect to y, you have to multiply the result with the derivative of y with respect to x, because, again, y is a function of x. Hope that's clear. thornahawk
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