Find the derivative $\frac{d}{dx}\left(\frac{3}{\ln\left(\sqrt{\sin\left(x\right)-\cos\left(x\right)}\right)}\right)$

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$\frac{d}{dx}\left(\frac{3}{\frac{1}{2}\ln\left(\sin\left(x\right)-\cos\left(x\right)\right)}\right)$

Learn how to solve integral calculus problems step by step online. Find the derivative d/dx(3/ln((sin(x)-cos(x))^1/2)). Simplify the derivative by applying the properties of logarithms. Simplify the division 3 by \frac{1}{2}. 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 constant function (6) is equal to zero.