A doubt in Partial Differentiation

babbar.ankit
Posts: 5
Joined: Sat May 29, 2010 11:56 am

A doubt in Partial Differentiation

Postby babbar.ankit » Thu Aug 05, 2010 2:00 pm

Can some one help me understand how partial derivative work in case of dependent variables...
∂f(y+ßµ,y´+ßµ´,x)/∂ß=???
µ(x),y(x)

CyberShot
Posts: 23
Joined: Sat May 15, 2010 5:43 pm

Re: A doubt in Partial Differentiation

Postby CyberShot » Thu Sep 09, 2010 6:32 pm

I'm assuming you mean ∂/∂ß of three different functions, y+ßµ, y´+ßµ´and x

In this case, treat every variable except ß as a constant.

∂/∂ß of y+ßµ = ß and so on

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twistor
Posts: 1531
Joined: Thu Apr 13, 2006 2:47 pm

Re: A doubt in Partial Differentiation

Postby twistor » Fri Sep 10, 2010 12:11 pm

Think of it like this:

f(y + beta*mu, y' + beta*mu', ..., x)

let u(y,beta,mu) = y + beta*mu, etc.

then f = f(u,u',...,x)

When you take the partials with respect to beta you apply the chain rule as usual for partial differentiation.

i.e.

df/d(beta) = df/du du/d(beta) + df/du' du'/d(beta) + ...




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