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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$
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$5\frac{d}{dx}\left(\sin\left(x\right)+\cos\left(x\right)\right)\left(\sin\left(x\right)-\cos\left(x\right)\right)+\left(\sin\left(x\right)+\cos\left(x\right)\right)\left(5\frac{d}{dx}\left(\sin\left(x\right)-\cos\left(x\right)\right)+\frac{d}{dx}\left(5\right)\left(\sin\left(x\right)-\cos\left(x\right)\right)\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(5(sin(x)+cos(x))(sin(x)-cos(x))). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The derivative of the constant function (5) is equal to zero. Any expression multiplied by 0 is equal to 0. x+0=x, where x is any expression.