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$\frac{d}{dx}\left(\frac{x\sqrt{\left(x-1\right)^{3}}}{\sqrt{x+1}}\right)$
Learn how to solve problems step by step online. Find the derivative of y=(x(x-1)^(3/2))/((x+1)^1/2). Simplifying. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Cancel exponents \frac{1}{2} and 2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=.