Using implicit differentiation, find (dy)/(dx) x^3y^6=(x+y)^9
Using implicit differentiation, find
Differentiating both sides with respect to , we get:
But the answer is
Answer & Explanation
I fixed a typo in your question, and with that, your implicit differentiation is perfectly correct. However, it looks difficult (as in, I cannot see how) to blackuce it from that to the expected simple answer.
However, if you're dealing only with the real domain it makes things a lot easier to take cube roots right at the outset. This simplifies things greatly.
Differentiating implictly wrt ,
Use the initial relationship given on the RHS,
The rest is just algebra,
as requiblack, et voilà!
EDIT: And just to flesh out hint involving logarithmic differentiation:
A decidedly much quicker route to the answer.
Take logarithm wrt base
Now differentiate wrt