Derivative of $$$y^{\frac{5}{2}}$$$
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Find $$$\frac{d}{dy} \left(y^{\frac{5}{2}}\right)$$$.
Solution
Apply the power rule $$$\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$$$ with $$$n = \frac{5}{2}$$$:
$${\color{red}\left(\frac{d}{dy} \left(y^{\frac{5}{2}}\right)\right)} = {\color{red}\left(\frac{5 y^{\frac{3}{2}}}{2}\right)}$$Thus, $$$\frac{d}{dy} \left(y^{\frac{5}{2}}\right) = \frac{5 y^{\frac{3}{2}}}{2}$$$.
Answer
$$$\frac{d}{dy} \left(y^{\frac{5}{2}}\right) = \frac{5 y^{\frac{3}{2}}}{2}$$$A