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The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if ${f(x) = \sin(x)}$, then ${f'(x) = \cos(x)\cdot D_x(x)}$
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$\frac{d}{dx}\left(2x\right)\cos\left(2x\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(sin(2x)). The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=2 and g=x. The derivative of the constant function (2) is equal to zero. Any expression multiplied by 0 is equal to 0.