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Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(\frac{\frac{1}{-\frac{1}{2}+x}+2}{x}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (1/(-1/2+x)+2)/x. Simplifying. Combine \frac{1}{-\frac{1}{2}+x}+2 in a single fraction. Divide fractions \frac{\frac{1+2\left(-\frac{1}{2}+x\right)}{-\frac{1}{2}+x}}{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}}.