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Problem Given y = arccos ( 1 − 3 x 1 + 3 x ) y=\arccos\!\left(\dfrac{1-3x}{1+3x}\right) y = arccos ( 1 + 3 x 1 − 3 x ) d y d x \dfrac{dy}{dx} d x d y − 6 ( 1 + 3 x ) 2 1 − ( 1 − 3 x 1 + 3 x ) 2 -\dfrac{6}{(1+3x)^{2}\,\sqrt{1-\left(\dfrac{1-3x}{1+3x}\right)^{2}}} − ( 1 + 3 x ) 2 1 − ( 1 + 3 x 1 − 3 x ) 2 6 6 ( 1 + 3 x ) 2 1 − ( 1 − 3 x 1 + 3 x ) 2 \dfrac{6}{(1+3x)^{2}\,\sqrt{1-\left(\dfrac{1-3x}{1+3x}\right)^{2}}} ( 1 + 3 x ) 2 1 − ( 1 + 3 x 1 − 3 x ) 2 6 6 ( 1 + 3 x ) 1 − ( 1 − 3 x 1 + 3 x ) 2 \dfrac{6}{(1+3x)\,\sqrt{1-\left(\dfrac{1-3x}{1+3x}\right)^{2}}} ( 1 + 3 x ) 1 − ( 1 + 3 x 1 − 3 x ) 2 6 − 1 1 − ( 1 − 3 x 1 + 3 x ) 2 -\dfrac{1}{\sqrt{1-\left(\dfrac{1-3x}{1+3x}\right)^{2}}} − 1 − ( 1 + 3 x 1 − 3 x ) 2 1 Browse the problem library