[Implicit Differentiation] (5x-y)^4 + 2y^3 = 258 evaluate y' at the

Check that the point (1,1) satisfies the given equation, i.e. it is on the curve.

Use implicit differentiation to differentiate each term and obtain an equation containing x, y and y'.
Solve for y'.
You should get
y'=20(5x-y)³/(4(5x-y)³-6y²)
Substitute (1,1) into the above equation to get y'(1,1)=128/25.

Check my calculations.

Thanks. Correct.

You're welcome!