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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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
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$\frac{\frac{d}{dx}\left(3\right)\ln\left(\sqrt{\sin\left(x\right)-\cos\left(x\right)}\right)-3\frac{d}{dx}\left(\ln\left(\sqrt{\sin\left(x\right)-\cos\left(x\right)}\right)\right)}{\ln\left(\sqrt{\sin\left(x\right)-\cos\left(x\right)}\right)^2}$
Learn how to solve problems step by step online. Find the derivative using the quotient rule d/dx(3/ln((sin(x)-cos(x))^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 (3) is equal to zero. Any expression multiplied by 0 is equal to 0. x+0=x, where x is any expression.