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It is not totally clear to what the square root applies*; if just the 2, then:
d/dx ((√2)sin x) = (√2) cos x
if all of 2 sin x, then:
d/dx (√(2 sin x)) = cos x / √(2 sin x)
* for the second version I would expect "square root all of 2 sin x" but some people would write as given in the question meaning this, so I've given both just in case.
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What is sin 60 degrees?
square root 3/2
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What is the derivative of the square root of cos x?
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d/dx [sin(x) + 2] = cos(x)
What is the derivative of y equals sin times x to the power of 2?
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