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.