$\frac{7x}{\sqrt[\phantom{2}]{x}}=7x^{\frac{1}{2}}$

$\frac{9}{\sqrt[\phantom{2}]{x}}=9x^{-\frac{1}{2}}$

Step $2$

Therefore, we have

$y=\frac{9x^{2}7x9}{\sqrt[\phantom{2}]{x}}=9x^{\frac{3}{2}}7x^{\frac{1}{2}}9x^{-\frac{1}{2}}$

Now, since the function is a sum of power functions, we can use the Power Rule to find its derivative. Recall that according to the Power Rule, the derivative of $x^n,$ where $n$ is any real number, is $n{x}^{n-1}.$ To use the Power Rule, we'll have to calculate the following.

$\frac{3}{2}-1=$

$\frac{1}{2}-1=$

$-\frac{1}{2}-1=$

Applying the Power Rule we have

$y^{\text{'}}=,x^{\frac{1}{2}},x^{-\frac{1}{2}}(,)x^{-\frac{3}{2}}$

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