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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 differential calculus problems step by step online. Find the derivative of 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)}. The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1. Any expression multiplied by 1 is equal to itself.