>_< I know how you feel xD
I tried implicit differentiation, but I don't think I'm doing it right. I've never done a question where the sin function has two variables (both x and y) in it, so I'm not really sure how that works. And moreover, I can't seem to get past the first step of the implicit differentiation because I don't know what to do next. :33
"implicit" means that it is "implied" that is a function of . This means that when and are grouped together as a product, quotient, etc... it must be understood that one must employ the neccesary and appropriate method of differetiating.
For example, consider the function
Taking the derivative is simple enough
Well, what if we had simply rewrote before differentiating, and subtracted from both sides
No problem, is still a function of , so the derivative "with respect to x" is
And adding, we are back to where we started
.
In this case, it was very easy to solve for , but sometimes - as in the problem you have provided - solving for is tedious, and in some cases, impossible. So, we understand to be an "implied" function of and we differentiate.
Bye!