Hello. My problem is as follows: Suppose x^4+y^2+y-3=0. a) Compute dy/dx by implicit differentiation. b) What is dy/dx when x=1 and y=1? c) Solve for y in terms of x (by the quadratic formula) and compute dy/dx directly. Compare with your answer in part a).
I solved a) and b). a)=-4x^3/(2y + 1), and b)=-4/3. I'm stuck at c). This is what I've been doing: Using the quadratic formula to solve for y in x^4+y^2+y-3=0 gives y=-1±√-4x^4+13/(2). Then applying the chain rule in the result of y gives -4x^3/(√-4x^4+13). But it must give the same as a)=-4x^3/(2y + 1) . Where am I failing at? How can I solve it?
Thank you for your time.

Hello, KFs, and welcome to ScienceForums.

You have done some good work and congratualtions on posting your attempt.

So why not amaze yourself and finish the job?

When x = 1

[math]\frac{{ - 4{x^3}}}{{\sqrt { - 4{x^4} + 13} }} = \frac{{ - 4}}{{\sqrt { - 4 + 13} }}[/math]

Which you have already calculated.