1 1+x The result from the differentiation is dy Derive the formula = dx Solve for dy dx secy = 1 Therefore, dy dx dy 1 dx secy = = Now, perform a trigonometric substitution for sec y. secy= dy 1 dx 1 + tan y 1 2 1+tan y 1 1+ for the derivative of y = tan = 1. Divide both sides by secy. Recall that tan y = x. -1 'x by differentiating both sides of the equivalent equation tan y = x. Substitute x for tan y.