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Derivative of $$$t^{\frac{7}{2}}$$$
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Your Input
Find $$$\frac{d}{dt} \left(t^{\frac{7}{2}}\right)$$$.
Solution
Apply the power rule $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ with $$$n = \frac{7}{2}$$$:
$${\color{red}\left(\frac{d}{dt} \left(t^{\frac{7}{2}}\right)\right)} = {\color{red}\left(\frac{7 t^{\frac{5}{2}}}{2}\right)}$$Thus, $$$\frac{d}{dt} \left(t^{\frac{7}{2}}\right) = \frac{7 t^{\frac{5}{2}}}{2}$$$.
Answer
$$$\frac{d}{dt} \left(t^{\frac{7}{2}}\right) = \frac{7 t^{\frac{5}{2}}}{2}$$$A