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using the chain rule let tanx = u, then y = u^2
du/dx = sec^2x and dy/du = 2u
dy/dx = dy/du * du/dx = 2 tanx sec^2x
derivate the outside....you will get the 2 as a coefficient and subtract 1 from the previous power..to get 2tanx....derivate the inside you will get sec^2x...multiply the two....to get dy/dx=2tanxsec^2x