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$\frac{d}{dx}\left(\frac{\left(x-1\right)^{32}\sqrt{\left(x+1\right)^{3}}}{\left(x^2+3x+3\right)^{17}}\right)$
Learn how to solve problems step by step online. Find the derivative of ((x-1)^32(x+1)^(3/2))/((x^2+3x+3)^17). 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}}. Simplify \left(\left(x^2+3x+3\right)^{17}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 17 and n equals 2. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(x-1\right)^{32} and g=\sqrt{\left(x+1\right)^{3}}.