Prove that if \( f(x)=\frac{1}{4 \sqrt{2}} \log \frac{x^{2}+\sqrt{2} x+1}{x^{2}-\sqrt{2} x+1}+\frac{1}{2 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{1-x^{2}}\right) \), then \( f^{\prime}(x)=\frac{1}{1+x^{4}} \).

Question

Q22. Prove that if \( f(x)=\frac{1}{4 \sqrt{2}} \log \frac{x^{2}+\sqrt{2} x+1}{x^{2}-\sqrt{2} x+1}+\frac{1}{2 \sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2} x}{1-x^{2}}\right) \), then \( f^{\prime}(x)=\frac{1}{1+x^{4}} \).