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Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$
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$derivdef\left(\sin\left(x\right)\frac{\cos\left(x\right)}{\sin\left(x\right)}\right)$
Learn how to solve problems step by step online. Find the derivative of sin(x)cot(x) using the definition. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Multiplying the fraction by \sin\left(x\right). Simplify the fraction \frac{\cos\left(x\right)\sin\left(x\right)}{\sin\left(x\right)} by \sin\left(x\right). Find the derivative of \cos\left(x\right) using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is \cos\left(x\right). Substituting f(x+h) and f(x) on the limit, we get.