Final answer to the problem
$\frac{-x\arccos\left(x\right)}{\sqrt{1-x^2}}-1$
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Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative of (1-x^2)^(1/2)arccos(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sqrt{1-x^2} and g=\arccos\left(x\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.
Final answer to the problem
$\frac{-x\arccos\left(x\right)}{\sqrt{1-x^2}}-1$
