Dear Student, y = lnx+x2+a2dydx= 1x+x2+a2×ddxx+x2+a2=1x+x2+a2×ddxx+ddxx2+a2=1x+x2+a2×1+xx2+a2=1x+x2+a2×x+x2+a2x2+a2=1x2+a2Regards

Find dy/dx

Dear Student, y = \ln (x + \sqrt{x^{2} + a^{2}}) \frac{dy}{dx} = \frac{1}{(x + \sqrt{x^{2} + a^{2}})} \times \frac{d}{dx} (x + \sqrt{x^{2} + a^{2}}) = \frac{1}{(x + \sqrt{x^{2} + a^{2}})} \times [\frac{d}{dx} x + \frac{d}{dx} \sqrt{x^{2} + a^{2}}] = \frac{1}{(x + \sqrt{x^{2} + a^{2}})} \times [1 + \frac{x}{\sqrt{x^{2} + a^{2}}}] = \frac{1}{(x + \sqrt{x^{2} + a^{2}})} \times [\frac{x + \sqrt{x^{2} + a^{2}}}{\sqrt{x^{2} + a^{2}}}] = \frac{1}{\sqrt{x^{2} + a^{2}}} Regards