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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\left(-\frac{2}{3}\sec\left(2x\right)\right)^3\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (1/3sec(2x)-sec(2x))^3. Simplify the derivative by applying the properties of logarithms. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant (-\frac{8}{27}) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.