If , then
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
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.