Final Answer
Step-by-step Solution
Specify the solving method
Simplifying
Learn how to solve problems step by step online.
$\frac{d}{dx}\left(\frac{\left(x-1\right)\left(2x-2\right)-2x^2+4x+6}{\left(x-1\right)^{3}}\right)$
Learn how to solve problems step by step online. Find the derivative using the quotient rule d/dx(((x-1)^2(2x-2)-2(x^2-2x+-3)(x-1))/((x-1)^4)). 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-1\right)^{3}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals 2. Simplify the product -(\left(x-1\right)\left(2x-2\right)-2x^2+4x+6).