I am reposting this question because one reply was an answer of 10/(y^3) for dy/

Question

I am reposting this question because one reply was an answer of 10/(y^3) for dy/dx and another one was dy/dx = -(2x + 2y + 1)/(2x - 2y). So, I would appreciate if anyone can clarify which should be the correct answer. The person answering 10/(y^3) did not use implicit differentiation but their answer matches what I can get on Wolfram Alpha ! The person answering dy/dx = -(2x + 2y + 1)/(2x - 2y) showed steps beautifully. Who is right? Whoever clarifies, please show steps.
Here is the question again - Using implicit differentiation, find derivative dy/dx and the slope of the curve at the given point. y^4 =40x; (250,10)
Please keep in mind what I explained regarding previous responses.

Explanation / Answer

If y^4 = 40x, then the implicit differentiation is 4y^3dy = 40dx (If you wish, you can first move 40x to the other side and get y^4 - 40xdx = 0, then write 4y^3dy -40dx = 0; you then move 40dx to the other side and get the equation 4y^3dy=40dx as written above) Thus, dividing by 4y^3dx on both sides to simplify, you get dy/dx = 40/4y^3 = 10/y^3 Now, you can plug in the point (250, 10) to get the slope, or the derivative at the point. It is 10/y^3 = 10/10^3 = 1/10^2 = 1/100

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