Решете d/dxleft(arctan(sqrt{1-sin(x)/1+sin(x)})right)

$$\frac{d}{d x } \left( \arctan ( \sqrt{ \frac{ 1- \sin ( x ) }{ 1+ \sin ( x ) } } ) \right)$$

Процени

$$-\frac{\cos(x)}{2\left(\sin(x)+1\right)\sqrt{\frac{-\sin(x)+1}{\sin(x)+1}}}$$

Диференцирај во однос на x

$$\frac{-\frac{\left(\cos(x)\right)^{2}}{\left(\sin(x)+1\right)^{3}\times \left(\frac{-\sin(x)+1}{\sin(x)+1}\right)^{\frac{3}{2}}}+\frac{\sin(x)}{\left(\sin(x)+1\right)^{3}\times \left(\frac{-\sin(x)+1}{\sin(x)+1}\right)^{\frac{3}{2}}}-\frac{\left(\frac{\sin(x)}{\sin(x)+1}\right)^{3}}{\left(\frac{-\sin(x)+1}{\sin(x)+1}\right)^{\frac{3}{2}}}+\frac{\left(\cos(x)\right)^{2}}{\sqrt{\left(-\sin(x)+1\right)\left(\sin(x)+1\right)^{3}}}}{2}$$