# How do you find the derivative of #y =sqrt(5x)#?

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To find the derivative of ( y = \sqrt{5x} ), we can use the power rule for differentiation. The power rule states that if we have a function of the form ( f(x) = x^n ), then its derivative is given by ( f'(x) = nx^{n-1} ). Applying this rule to the given function:

( y = \sqrt{5x} )

We rewrite the function as:

( y = (5x)^{\frac{1}{2}} )

Now, applying the power rule:

( y' = \frac{1}{2}(5x)^{\frac{1}{2} - 1} \cdot 5 )

( y' = \frac{1}{2} \cdot 5 \cdot (5x)^{-\frac{1}{2}} )

( y' = \frac{5}{2} \cdot \frac{1}{\sqrt{5x}} )

( y' = \frac{5}{2\sqrt{5x}} )

So, the derivative of ( y = \sqrt{5x} ) with respect to ( x ) is ( \frac{5}{2\sqrt{5x}} ).

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