X^6 + y^6 = 1

What does:

y'' =

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