Evaluate
\frac{-\sqrt{2\left(-\sin(x)+1\right)}\ln(\frac{\sqrt{-\sin(x)+1}|\frac{-\sqrt{2\left(-\sin(x)+1\right)}+1}{\sqrt{-\sin(x)+1}}|}{\sqrt{2\left(-\sin(x)+1\right)}+1})+1}{\sqrt{-\sin(x)+1}}+С
Differentiate w.r.t. x
\frac{\cos(x)\left(2\sqrt{2\left(-\sin(x)+1\right)}|\frac{-\sqrt{2\left(-\sin(x)+1\right)}+1}{\sqrt{-\sin(x)+1}}|-2\sqrt{-\sin(x)+1}sign(\frac{-\sqrt{2\left(-\sin(x)+1\right)}+1}{\sqrt{-\sin(x)+1}})-\sqrt{2}sign(\frac{-\sqrt{2\left(-\sin(x)+1\right)}+1}{\sqrt{-\sin(x)+1}})+|\frac{-\sqrt{2\left(-\sin(x)+1\right)}+1}{\sqrt{-\sin(x)+1}}|\right)}{2\left(\sqrt{2\left(-\sin(x)+1\right)}+1\right)|\frac{-\sqrt{2\left(-\sin(x)+1\right)}+1}{\sqrt{-\sin(x)+1}}|\left(-\sin(x)+1\right)^{\frac{3}{2}}}
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