Question

The differential coefficient of ${\displaystyle {\text{tan}}^{-1}\left(\frac{\sqrt{1+\text{x}}-\sqrt{1-\text{x}}}{\sqrt{1+\text{x}}+\sqrt{1-\text{x}}}\right)}$ is ____________.

विकल्प

• ${\displaystyle \sqrt{1-{\text{x}}^2}}$

• ${\displaystyle \frac{1}{\sqrt{1-{\text{x}}^2}}}$

• ${\displaystyle \frac{1}{2\sqrt{1-{\text{x}}^2}}}$

• x

Answer 1

The differential coefficient of ${\displaystyle {\text{tan}}^{-1}\left(\frac{\sqrt{1+\text{x}}-\sqrt{1-\text{x}}}{\sqrt{1+\text{x}}+\sqrt{1-\text{x}}}\right)}$ is ${\displaystyle \underline{\frac{1}{2\sqrt{1-{\text{x}}^2}}}}$.