Let g(x)=(sin(x))/(sqrtx). g^(')(x)=

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Let  g(x)=(sin(x))/(sqrtx).  g^(')(x)=

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Use Quotient Rule: To find the derivative of the function g(x) = (sin(x))/(sqrt(x)), we will use the quotient rule. The quotient rule states that if you have a function h(x) = f(x)/g(x), then h'(x) = (f'(x)g(x) - f(x)g'(x))/(g(x))^2. Here, f(x) = sin(x) and g(x) = sqrt(x).Find f'(x): First, we need to find the derivative of f(x) = sin(x). The derivative of sin(x) with respect to x is cos(x). So, f'(x) = cos(x).Find g'(x): Next, we need to find the derivative of g(x) = sqrt(x). The derivative of sqrt(x) with respect to x is 1/(2sqrt(x)). So, g'(x) = 1/(2sqrt(x)).Apply Quotient Rule: Now we apply the quotient rule. We have f'(x) = cos(x) and g'(x) = 1/(2sqrt(x)). Plugging these into the quotient rule formula, we get:  g'(x) = (cos(x) * sqrt(x) - sin(x) * (1/(2sqrt(x)))) / (sqrt(x))^2.Simplify Expression: Simplify the expression by multiplying through by sqrt(x) and combining terms:  g'(x) = (cos(x) * sqrt(x) * sqrt(x) - sin(x) * (1/2)) / (x).  This simplifies to:  g'(x) = (cos(x) * x - sin(x) / 2) / x.Final Derivative: Finally, we can simplify the expression further by dividing each term by x:  g'(x) = cos(x) - (sin(x) / (2x)).  This is the derivative of g(x).

Let $g(x)=\frac{\sin (x)}{\sqrt{x}}$ . $\newline$ $g^{\prime}(x)=$

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