If $\phi(x)=\frac{1}{\sqrt{x}} \int\limits_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x>0$, then $\emptyset^{\prime}\left(\frac{\pi}{4}\right)$ is equal to :

Question

If $\phi(x)=\frac{1}{\sqrt{x}} \int\limits_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x>0$,

then $\emptyset^{\prime}\left(\frac{\pi}{4}\right)$ is equal to :

$\frac{4}{6+\sqrt{\pi}}$

$\frac{4}{6-\sqrt{\pi}}$

$\frac{8}{\sqrt{\pi}}$

$\frac{8}{6+\sqrt{\pi}}$

Solution

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