Find the derivative of $a\left(\left(\sin\left(bs45\right)+\cos\left(45\right)\right)\frac{1}{x-1}- \left(\cos\left(45\right)-\sin\left(45\right)\right)\left(x^2+1\cdot -2x+1\right)\right)$

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$\frac{d}{da}\left(a\left(\left(\sin\left(bs45\right)+\cos\left(45\right)\right)\frac{1}{x-1}- \left(\cos\left(45\right)-\sin\left(45\right)\right)\left(x^2-2x+1\right)\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of a((sin(bs45)+cos(45))1/(x-1)-(x^2+1*-2x+1)(cos(45)-sin(45))). Simplifying. 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 the product -(\sin\left(bs45\right)+\frac{\sqrt{2}}{2}).