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Question Number 113330 by mathdave last updated on 12/Sep/20

Answered by MJS_new last updated on 12/Sep/20

use formula for half derivate  (d^q /dx^q )x^p =((Γ (p+1))/(Γ (p−q+1)))x^(p−q)   ⇒  answer is ((Γ (3))/(Γ ((5/2))))x^(3/2) =(8/(3(√π)))x^(3/2)

$$\mathrm{use}\:\mathrm{formula}\:\mathrm{for}\:\mathrm{half}\:\mathrm{derivate} \\ $$$$\frac{{d}^{{q}} }{{dx}^{{q}} }{x}^{{p}} =\frac{\Gamma\:\left({p}+\mathrm{1}\right)}{\Gamma\:\left({p}−{q}+\mathrm{1}\right)}{x}^{{p}−{q}} \\ $$$$\Rightarrow \\ $$$$\mathrm{answer}\:\mathrm{is}\:\frac{\Gamma\:\left(\mathrm{3}\right)}{\Gamma\:\left(\frac{\mathrm{5}}{\mathrm{2}}\right)}{x}^{\mathrm{3}/\mathrm{2}} =\frac{\mathrm{8}}{\mathrm{3}\sqrt{\pi}}{x}^{\mathrm{3}/\mathrm{2}} \\ $$

Commented by mathdave last updated on 13/Sep/20

correct

$${correct} \\ $$

Commented by Tawa11 last updated on 06/Sep/21

great sir

$$\mathrm{great}\:\mathrm{sir} \\ $$

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