Transposing Equations?

Hopefully I word this the right way.

Solving algebraic equations is an easy task, if you have a formula like the one for momentum in physics; p = mv, to solve for v, you just divide through by m on the LHS and RHS, and you get v = p /m. "Whatever you do to one side, you do to the other" - we all know that. Simple as pie.

However, when you get an equation that involves more than just your typical algebra, like one with integrals in it, and they ask you to solve for a certain term, say the term in the integrand, do you have to differentiate both sides of the equation, and then continue to rearrange it to get the desired subject like you would with a more simple equation?

I've gotten hung up on this before when manipulating larger, more complex formulas involving derivatives and integrals and was curious about it.

Thanks in advance for any answers.