# Math Help - Implicit differentiation

1. ## Implicit differentiation

For some questions on finding dy/dx implicitly, e.g. $\sqrt{1+x^{2}y^{2}}=2xy$, it is easier if we square both sides first.

My question is this, when I square both sides of the equation, will I ALWAYS get the correct dy/dx? Will I "change" the question if I square both sides?

Thanks!

2. Originally Posted by acc100jt
For some questions on finding dy/dx implicitly, e.g. $\sqrt{1+x^{2}y^{2}}=2xy$, it is easier if we square both sides first.

My question is this, when I square both sides of the equation, will I ALWAYS get the correct dy/dx? Will I "change" the question if I square both sides?

Thanks!
As is often the case when you square both sides of an equation to make caculations easier, you may get extraneous answers.

3. To clarify on what Prove It said, you may arrive at extraneous solutions in addition to the valid solution(s), but the valid solution(s) (if any exist) will not be lost.