If , then

- (A)
- (B)
- (C)
- (D)
- (A)

- Nov 7th 2009, 04:27 PMStarlitxSunshineImplicit Differentiation of a Trignometric Equation [Multiple Choice]
If , then

- (A)
- (B)
- (C)
- (D)
- (A)

- Nov 7th 2009, 04:31 PMVonNemo19
- Nov 7th 2009, 04:33 PMapcalculus
- Nov 7th 2009, 04:39 PMStarlitxSunshine
>_< 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 - Nov 7th 2009, 04:51 PMVonNemo19
"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!