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