Question

If y= tan–¹x, then dy/dx is

Answer 1

Answer:

y = Tan⁻¹x

Taking Tan both sides,

⇒ Tan y = x

Differentiating both side w.r.t x

⇒ Sec²y dy/dx  = 1

Using Sec²y = 1 + Tan²y

⇒ (1  + Tan²y) dy/dx  = 1

As we know, Tan y = x

⇒ Tan²y = x²

⇒ (1 + x²)dy/dx  = 1

⇒ dy/dx = (1 + x²)⁻¹