Final Answer
Step-by-step Solution
Specify the solving method
Combine $\frac{1}{\left(2-x\right)^2}-\frac{1}{4}$ in a single fraction
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(\frac{\frac{1-\frac{1}{4}\left(2-x\right)^2}{\left(2-x\right)^2}}{x}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (1/((2-x)^2)-1/4)/x. Combine \frac{1}{\left(2-x\right)^2}-\frac{1}{4} in a single fraction. Divide fractions \frac{\frac{1-\frac{1}{4}\left(2-x\right)^2}{\left(2-x\right)^2}}{x} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. 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}}. The power of a product is equal to the product of it's factors raised to the same power.