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$\frac{d}{dx}\left(x-2\left(x-1\right)^{-\frac{1}{2}}\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(x-2(x-1)^(1/2-1)) using the sum rule. Simplifying. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=-2 and g=\left(x-1\right)^{-\frac{1}{2}}. The derivative of the constant function (-2) is equal to zero.