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Multiply the single term $\cot\left(x\right)^2$ by each term of the polynomial $\left(\sec\left(x\right)^2-1\right)$
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$derivdef\left(\sec\left(x\right)^2\cot\left(x\right)^2-\cot\left(x\right)^2\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of cot(x)^2(sec(x)^2-1) using the definition. Multiply the single term \cot\left(x\right)^2 by each term of the polynomial \left(\sec\left(x\right)^2-1\right). \sec\left(x\right)^2\cot\left(x\right)^2 simplifies to cosecant \csc\left(x\right). \csc\left(x\right)^2-\cot\left(x\right)^2 is equal to 1. Find the derivative of 1 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 1. Substituting f(x+h) and f(x) on the limit, we get.