Before taking the derivatives of the function, simplify the equation first for smooth operation.
x^6 + y^6 = 1
Multiply the whole equation with an exponent of 1/6 for uniformity. This would get rid of the exponents of x and y. The product would be
x + y = 1^1/6
x + y = 1
Expressing in terms of x:
y = 1 - x
Now, we derive the equation:
y' = 0 -1 = -1
y" = 0