Feasibility of finding public key when private key is known We all know that in a public key cryptosystem, given a public key it is extremely hard to compute private key from it.

Is it the same case in reverse?

Given a private key, how easy is it to compute public key out of it?

It would be great to have answers with respect to an algorithm like RSA.
In practice, no.

Firstly, RSA private keys are typically stored together with the public exponent. The standard definition includes the following information:

RSAPrivateKey ::= SEQUENCE {
  version           Version, 
  modulus           INTEGER,  -- n
  publicExponent    INTEGER,  -- e
  privateExponent   INTEGER,  -- d
  prime1            INTEGER,  -- p
  prime2            INTEGER,  -- q
  exponent1         INTEGER,  -- d mod (p-1)
  exponent2         INTEGER,  -- d mod (q-1) 
  coefficient       INTEGER,  -- (inverse of q) mod p
  otherPrimeInfos   OtherPrimeInfos OPTIONAL 
}


Obviously, if this is the information you got, deriving the public key is just a matter of extracting the fields modulus and publicExponent.

Secondly, the public exponent is typically a small pre-defined value, selected for making the public key operation as efficient as possible. Even if all information you got in the private key is modulus and privateExponent, it would be trivial to test the two most common publicExponent values $3$ and $65537$ and see if they check out. If not, the publicExponent is rarely greater than $2^{32}$, so checking every such odd value would still be feasible. 

Checking if a known privateExponent matches a guessed publicExponent, is typically just a matter of performing a RSA encryption of arbitrary data with one key, and test if the resulting cipher text can be decrypted with the other.

Thirdly, should the publicExponent deliberatly be selected as a random value roughly the same size as the modulus, then deriving publicExponent from privateExponent and modulus, would indeed be as hard as deriving privateExponent from publicExponent and modulus. This is however not how RSA is typically used or how RSA keys are typically generated.