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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 d/dx((1/3sec(2x)-sec(2x))^3). Simplifying. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Taking the derivative of secant function: \frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x).