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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\sin\left(\frac{2\left(1-\ln\left(x\right)\right)}{x}\right)\right)$
Learn how to solve problems step by step online. Find the derivative of sin(2(1-ln(x))/x). Simplify the derivative by applying the properties of logarithms. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. 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 derivative of the linear function is equal to 1.