Odisha Board Solutions for Chapter: Continuity and Differentiability, Exercise 5: EXERCISE 7(e)

Differentiate the following function by proper substitution: ${\tan }^{-1}\sqrt{\frac{1-t}{1+t}}$.

Differentiate the following function: ${\left[{\left(\frac{1+t^2}{1-t^2}\right)}^2-1\right]}^{\frac{1}{2}}$.

Differentiate the following function by proper substitution: ${\tan }^{-1}\left(\frac{\sqrt{x}+\sqrt{a}}{1-\sqrt{xa}}\right)$.

Differentiate the following function by proper substitution: ${\sin }^{-1}\left(\frac{2x}{1+x^2}\right)$.

Differentiate the following function by proper substitution: ${\sec }^{-1}\left(\frac{\sqrt{a^2+x^2}}{a}\right)$.

Differentiate the following function by proper substitution: ${\sin }^{-1}\left(\frac{2\sqrt{t^2-1}}{t^2}\right)$.

Differentiate the following function by proper substitution: ${\cos }^{-1}\left(\frac{1-t^2}{1+t^2}\right)$.

Differentiate the following function by proper substitution: ${\cos }^{-1}\left(2t^2-1\right)$.