# How do you find the derivative with a square root in the denominator #y= 5x/sqrt(x^2+9)#?

The Quotient Rule says

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To find the derivative of the function ( y = \frac{5x}{\sqrt{x^2 + 9}} ) with a square root in the denominator, we can use the quotient rule. Let ( u = 5x ) and ( v = \sqrt{x^2 + 9} ). Then, ( u' = 5 ) and ( v' = \frac{x}{\sqrt{x^2 + 9}} ).

Now, applying the quotient rule:

[ y' = \frac{u'v - uv'}{v^2} = \frac{5\sqrt{x^2 + 9} - \frac{5x^2}{\sqrt{x^2 + 9}}}{x^2 + 9} ]

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