 In this video, we will provide the solution to question number 13 for the practice final exam for math 1210 We're given the the curve x to the two-thirds power plus y to the two-thirds power is equal to two We're asked to find the derivative that is dy over dx at the point One comma one so we have to compute the derivative implicitly in this situation So we're going to take the derivative of the left-hand side and we're going to do it with the right-hand side as well The derivative of the right-hand side is easy enough. It's gonna be zero since it's constant since we're taking the derivative There's with respect to x right here We do need to make sure we take y primes when we take derivatives of a y So the derivative of x to the two-thirds will be two-thirds x to the negative one-third The derivative of y to the two-thirds will be similar It's two-thirds y to the negative one-third. We have to also times that by y prime All right now we could solve for y prime at this moment, but since we don't need a we don't actually need to find dy dy over dx in general We only have to find at the point x equals one and y equals one So since the calculus part of the problem is done We can now plug in x equals one and y equals one to the problem in particular one to the one-third power is Going to be to the negative one-third power is going to be one So we see that this becomes two-thirds plus two-thirds y prime equals zero So track two-thirds from both sides So we skip two-thirds y prime equals negative two-thirds and so we then divide both sides by two-thirds and get that Y prime is equal to negative one which then tells us the correct answer was choice B