Find the derivative of $\sin\left(x\right)\cos\left(x\right)$

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Learn how to solve product rule of differentiation problems step by step online. Find the derivative of sin(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=\cos\left(x\right). 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)}. When multiplying two powers that have the same base (\cos\left(x\right)), you can add the exponents. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x).