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Learn how to solve differential calculus problems step by step online. Find the derivative of cos(t)cot(t)(sec(t)-2tan(t)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). Simplify the product -(\sec\left(\theta\right)-2\tan\left(\theta\right)). Taking the derivative of cotangent.
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The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.