Starting with Y prime, we're going to bring down the power and take the parenthesis portion to the one less power by using the power rule. And then we need to take the derivative of the inside by using the chain rule. So Y prime is going to equal three times the quantity 1 + 5 / X ^2. And then the derivative of the inside the derivative of a constant zero and the derivative of 5 / X is going to be -5 / X ^2. We could think of that by doing the quotient rule. Or we could also think of that as derivative of 1 / X. We could think of as the derivative of X to the -1 and doing the power rule there we bring down the exponent and take it to 1 less power, so that would be negative over X ^2. So once we simplify that up three times, the -5 / X ^2 is going to give us -15 / X ^2 times the quantity 1 + 5 X over 2. From there we need to take the 2nd derivative. So it's going to be the derivative the first times the second plus the derivative of the second times the 1st. So when we take the derivative of that first part -15 / X ^2, think of that X ^2 as X to the -2 and do the power rule. So we get 30 / X ^3 times the 1 + 5 / X ^2 plus the derivative of the second term. So we bring down the two, take it to the one less power, and that multiplies by the inside derivative by the chain rule times the -15 / X ^2. So the derivative of that inside portion, just like before, is going to be 0 -, 5 / X ^2. So when we do some multiplication and combining, we get 30 / X ^3 times the quantity 1 + 5 / X ^2 plus the quantity one 5150 / X to the fourth times the quantity 1 + 5 / X. Now if we factor out the lowest exponent, we would pull out the constant of 30X to the 4th in the denominator is smaller than X to the third one plus 5X to the first power, first power. So what That leaves us as X * 1 + 5 / X + 5 X * 1 is ** times 5 / X is five plus another five is 10. So a final answer of Y double prime equal 30 / X to the fourth times the quantity 1 + 5 / X times the quantity X + 10. If you pay attention, that last polynomial when I factored everything out is actually. That last parenthesis is actually a polynomial.