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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
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$\frac{d}{dx}\left(\left(1-\cos\left(x\right)\right)^2\right)\left(\tan\left(x\right)^3-\sin\left(x\right)^3\right)+\left(1-\cos\left(x\right)\right)^2\frac{d}{dx}\left(\tan\left(x\right)^3-\sin\left(x\right)^3\right)$
Learn how to solve problems step by step online. Find the derivative using the quotient rule (1-cos(x))^2(tan(x)^3-sin(x)^3). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. 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 sum of two or more functions is the sum of the derivatives of each function. The derivative of a sum of two or more functions is the sum of the derivatives of each function.