Do you mean to write:
I need to find the derivative of the following function.
[tex] i think this can be simplified to
so would it be reasonable to use the product and chain rule to solve the derivative of the 2nd part of the equation and just generally derive the 1st part?
Implicit differentiation works, but I don't think that it's any extra work to evaluate the derivative explicitly. Your function is .
Start by letting so that . Then .
Now as for you will need to use the chain rule again. You should get .