Given the curve x = √(3y^4 + 2)

Question

i)obtain dx/dy
ii)x(dx/dy)=6y^3

My Answer:
i)6*(3y^4+2)^-1/2
ii) 6*(3y^4+2)^-1/2 *(3y^4+2)^1/2

Answer 1

not quite. Remember the chain rule

dx/dy = 6y^3*(3y^4+2)^-1/2
Now you can see that (ii) is true

Doing things implicitly, it's much clearer:

x^2 = 3y^4+2
2x dx/dy = 12y^3
dx/dy = 6y^3/x