Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §4.4 Inverses of Trigonometric Functions, #12 · Calculus · Differentiation rules

Take the … derivative of … by the chain rule

Take the $y$ derivative of $cos (cos^{- 1} y) = y$ by the chain rule. Check that $d (cos^{- 1} y) / d y = - 1/ 1 - y^{2}$ gives a correct result.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §4.4 Inverses of Trigonometric Functions, #12

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