Question Number 113330 by mathdave last updated on 12/Sep/20
Answered by MJS_new last updated on 12/Sep/20
$$\mathrm{use}\:\mathrm{formula}\:\mathrm{for}\:\mathrm{half}\:\mathrm{derivate} \\ $$$$\frac{{d}^{{q}} }{{dx}^{{q}} }{x}^{{p}} =\frac{\Gamma\:\left({p}+\mathrm{1}\right)}{\Gamma\:\left({p}−{q}+\mathrm{1}\right)}{x}^{{p}−{q}} \\ $$$$\Rightarrow \\ $$$$\mathrm{answer}\:\mathrm{is}\:\frac{\Gamma\:\left(\mathrm{3}\right)}{\Gamma\:\left(\frac{\mathrm{5}}{\mathrm{2}}\right)}{x}^{\mathrm{3}/\mathrm{2}} =\frac{\mathrm{8}}{\mathrm{3}\sqrt{\pi}}{x}^{\mathrm{3}/\mathrm{2}} \\ $$
Commented by mathdave last updated on 13/Sep/20
$${correct} \\ $$
Commented by Tawa11 last updated on 06/Sep/21
$$\mathrm{great}\:\mathrm{sir} \\ $$