Actually in case of partial derivative how can I expand this derivative??Is their chain rule is applicable?I just expand this when f( lamda,theta) = nothing is given.
For simplicity, write eta = x. Assume also that lambda = lambda(x), theta = theta (x). Then, I would say that it is
df/dx = (partial f/partial lambda)(d lambda/dx) + (partial f/partial theta)(d theta/dx).
above answer was for variables but not for constants.
If you give specific problem and wait for two weeks ,I will find time to give you the necessary expansion.
B.Rath
The question actually can't be answered reasonably if not some context is given. As you write, no additional information is available concerning f. This is OK.We do need information on eta,lambda,theta. Writing a partial derivative with respect to eta assumes that a set of other variables is agreed to be constant while eta varies. Mostly this information is to be inferred from the context. Mostly it is given by agreeing on some system of coordinates. If, for instance, we use polar coordinates (r,theta,phi) and see a partial differentiation with respect tor r this is to be understood as implying that theta and phi are held constant in a variation of r. Would we consider cylinder coordinates (r,phi,z) then the partial differentiation with respect to r would imply that phi and z are constant. Both situations have a clear and simple geometrical meaning -- each situation a different one. If in your example we had the information that (eta,lambda,theta) is a coordinate system in space we would get that your expression is simply 0. If the situation is different, the result will be different. Simply: write what you know about eta, lamda, theta and I'm confident that we will find a reasonable answer.
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