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Applying the trigonometric identity: $\sin\left(\theta \right)\csc\left(\theta \right) = 1$
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$derivdef\left(x\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of tan(x)+cot(x)=sin(x)xcsc(x) using the definition. Applying the trigonometric identity: \sin\left(\theta \right)\csc\left(\theta \right) = 1. Find the derivative of x 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 x. Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms x and -x. Simplify the fraction \frac{h}{h} by h.