Final answer to the problem
$5\cos\left(x\right)$
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Step-by-step Solution
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1
The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function
$5\frac{d}{dx}\left(\sin\left(x\right)\right)$
2
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 ${f'(x) = \cos(x)\cdot D_x(x)}$
$5\cos\left(x\right)$
Final answer to the problem
$5\cos\left(x\right)$