# How do you find the derivative of #1/2sin2x#?

The chain rule will be applied.

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To find the derivative of ( \frac{1}{2} \sin(2x) ), you can use the chain rule of differentiation. The derivative of ( \sin(2x) ) with respect to ( x ) is ( 2 \cos(2x) ) according to the derivative of sine function. Multiplying by the derivative of the inner function ( 2x ) with respect to ( x ), which is ( 2 ), we get ( 2 \cdot 2 \cos(2x) = 4\cos(2x) ). Therefore, the derivative of ( \frac{1}{2} \sin(2x) ) with respect to ( x ) is ( 4\cos(2x) ).

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