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)

## A doubt in Partial Differentiation

### Re: A doubt in Partial Differentiation

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

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

∂/∂ß of y+ßµ = ß and so on

### Re: A doubt in Partial Differentiation

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) + ...

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) + ...