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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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$\frac{\frac{d}{dt}\left(\tan\left(t\right)+\cot\left(t\right)\right)\cot\left(t\right)-\left(\tan\left(t\right)+\cot\left(t\right)\right)\frac{d}{dt}\left(\cot\left(t\right)\right)}{\cot\left(t\right)^2}$
Learn how to solve problems step by step online. Find the derivative of (tan(t)+cot(t))/cot(t). 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}}. Simplify the product -(\tan\left(t\right)+\cot\left(t\right)). Taking the derivative of cotangent. Simplify the product -(-\tan\left(t\right)-\cot\left(t\right)).