Math Problem Statement

Find the derivative of the function.

y = sin−1(cos−1(t))

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Inverse Trigonometric Functions
Chain Rule

Formulas

Derivative of sin^{-1}(x): d/dx(sin^{-1}(x)) = 1 / sqrt(1 - x^2)
Derivative of cos^{-1}(x): d/dx(cos^{-1}(x)) = -1 / sqrt(1 - x^2)
Chain Rule for differentiation: d/dx(f(g(x))) = f'(g(x)) * g'(x)

Theorems

Chain Rule

Suitable Grade Level

Grades 11-12 or introductory college-level calculus