Partial Derivatives and their Inverses?

[rollbackcc]

Hi I have a question about partial derivatives?

For example if I have a function x = r cos theta

for all functions, not just for this function will dx/d theta be the inverse of dtheta/dx, so 1 divided by dx/d theta will be d theta/ dx? Please help on this partial derivative question. Thanks.

also for example if i have a function x = p cosh (n) and i need to find the partial derivative dn/dx can i find the partial derivative dx/dn and do 1 divided by dx/dn to find dn/dx?

Please help me on this.

 

[tiny-tim]

hi rollbackcc!

no

1 = ∂θ/∂θ = ∂θ/∂x*∂x/∂θ + ∂θ/∂y*∂y/∂θ

(to put it another way: ∂x/∂θ is calculated keeping r constant, ∂θ/∂x is calculated keeping y constant …

a partial derivative is always calculated keeping all variables constant except the one you're differentiating wrt to)