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Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator
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$\frac{d}{dx}\left(\frac{\frac{\cos\left(x\right)-1}{\cos\left(x\right)}}{1+\frac{1}{\cos\left(x\right)}}\right)$
Learn how to solve problems step by step online. Find the derivative using the quotient rule (1+-1/cos(x))/(1+1/cos(x)). Combine all terms into a single fraction with \cos\left(x\right) as common denominator. Combine all terms into a single fraction with \cos\left(x\right) as common denominator. Simplify the fraction \frac{\frac{\cos\left(x\right)-1}{\cos\left(x\right)}}{\frac{\cos\left(x\right)+1}{\cos\left(x\right)}}. 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}}.