optimization with constraint

question: where Use chain rule to find . Solve for y in terms of x and use the constraint to find x and y to maximize z.
NOTE: these are normal derivatives, not partial

work:

I take the derivative and subsitute x back in to get
Then I set it equal to 0 to get

Looks good so far. To solve for y, use power properties. . You can multiply both sides by y^a, where a will both cancel one y term and make the other y^1, which is very convenient.