500 x 2

500x500xSince 500500 is constant with respect to xx, the derivative of 500x500x with respect to xx is 500ddx[1x]500ddx[1x].500ddx[1x]500ddx[1x]Rewrite 1x1x as x−1x-1.500ddx[x−1]500ddx[x-1]Differentiate using the Power Rule which states that ddx[xn]ddx[xn] is nxn−1nxn-1 where n=−1n=-1.500(−x−2)500(-x-2)Multiply −1-1 by 500500.−500x−2-500x-2Rewrite the expression using the negative exponent rule b−n=1bnb-n=1bn.−5001×2-5001x2Combine terms.Tap...