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PROBLEM: Implicitly differentiate the following expression: xy Solution: Rewriting the equation without the square root symbol, (xy) 1/2=2-. Now differentiating. d (xy)1/2 E- d dx dx Using product rule. (xy) -1/2 {( x 2 ) + y)=1+2y-2 2 Let dy dx =y' Then rewriting the above equation with y' it becomes (xy)-1/2 {(xy') + y} = = -2y-3y' Opening the brackets on the left-hand side, (xy)-1/2 {(xy') + y}= Evry 2vay Rewriting the above equation using the expression obtained after opening the brackets,2VXy EVxy 2Vy 2Vxy y y - AVXy= vxy-2y Wvxy y'= (xy-27\ 4vxy zy3 xxy vay-27 * 2yay 4vey xy3-4vxy y (vxy-2y) 2(xy]-4vxy) But y' = dx Therefore, dy ya(xy - 2y) dx 2(xy] - 4xy)