If x = log (1 + t^2), y = t – tan^-1 t, show that dy/dx = √(e^x - 1)/2

Question

If x = log (1 + t²), y = t – tan^-1 t, show that \(\frac{dy}{dx} = {\frac{\sqrt{e^x - 1}}{2}}\)

dy/dx = √(e^x - 1)/2

Answer 1

x = log (1 + t²), y = t – tan^-1 t

Differentiating x and y w.r.t. t, we get