Explanation: Note that d d x ( arccos ( x ) ) = − 1 √ 1 − x 2 . Then, by the chain rule d d x ( arccos ( 4 x 2 ) ) = 2 ⋅ ( arccos ( 4 x 2 ) ) ⋅ d d x ( arccos ( 4 x 2 ) ) . Then, by the chain rule again, d d x ( arccos ( 4 x 2 ) ) = − 1 √ 1 − 16 x 4 ⋅ d d x ( 4 x 2 ) , d d x ( arccos ( 4 x 2 ) ) = − 8 x √ 1 − 16 x 4 . Substituting, d d x ( arccos ( 4 x 2 ) ) = − 16 x ⋅ arccos ( 4 x 2 ) √ 1 − 16 x 4 .