Question #54416
1 Answer
To solve this problem I will use 3 techniques:

Implicit differentiation. This involves differentiation of both sides of the equation.

The product rule :
#(u.v)'=v.(du)/(dx)+u.(dv)/(dx)# 
The chain rule. This involves differentiation of the outer layer and multiplying by the derivative of the inner layer.
I will show how this applies to the 1st derivative then work through the 2nd.
Using rule 1 we can write:
I'll differentiate each term:
So:
Factorising we get:
Eqn 1.
Now we differentiate again using the same techniques:
This simplifies to:
So:
Eqn 2.
The original equation is
So if
We can put these values back into Eqn 1:
Hence
Since
So: