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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\sin\left(x\right)$ and $g=4\cos\left(x\right)$
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$4\frac{d}{dx}\left(\sin\left(x\right)\right)\cos\left(x\right)+\sin\left(x\right)\frac{d}{dx}\left(4\cos\left(x\right)\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(4sin(x)cos(x)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sin\left(x\right) and g=4\cos\left(x\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\cos\left(x\right) and g=4. The derivative of the constant function (4) is equal to zero. Any expression multiplied by 0 is equal to 0.