Find derivative of x^x + y^x + a^ x + b^y = a^b + b^a Share with your friends Share 1 Neha Sethi answered this Dear student, We have xx+yx+ax+by=ab+baLet u = xx; v = yx; w = ax; z = byNow, u + v + w + z = ab+ba⇒dudx + dvdx + dwdx + dzdx = ddxab+ba⇒dudx + dvdx + dwdx + dzdx = 0 .....1Now, u = xx⇒log u = x log x⇒1ududx = x×1x + log x⇒dudx = xx1 + log xNow, v = yx⇒log v = x log y⇒1vdvdx = x×1ydydx + log y⇒dvdx = yxxydydx + log y⇒dvdx = xyx-1dydx + yx log yNow, w = ax⇒dwdx = ax log aNow, z = by⇒log z = y log b⇒1zdzdx = y×0 + log b ×dydx⇒dzdx = by log bdydxNow, from 1, we getxx1 + log x + xyx-1dydx + yx log y + ax log a + by log bdydx = 0⇒xyx-1dydx + by log bdydx = -xx1 + log x - yx log y - ax log a⇒dydx = -xx1 + log x + yx log y + ax log axyx-1+ by log b Regards 1 View Full Answer Meethi answered this You need to take log. Try it again. 1