What is the derivative of f (x) = tan^-1 (x)?

Solution:

In mathematics, the inverse trigonometric function is also known as 'arc functions'. To find the derivative of f (x) = tan^-1 (x) we will use inverse identity.

f (x) = tan^-1 (x)

Let y = tan^-1 (x)

⇒ tan y = x

On differentiating both the sides with respect to 'x', we will get

sec² y.dy/dx = 1

⇒ dy/dx = 1 / sec² y

⇒ dy/dx = 1 / (1+ tan² y), ∵ 1+ tan² y = sec² y

Since tan y = x, we get

dy/dx = 1 / (1 + x²),

⇒ d/dx (tan^-1 (x) = 1 / (1 + x²)

Thus, the derivative of f (x) = tan^-1 (x) is 1/ (1 + x²)

What is the derivative of f (x) = tan^-1 (x)?

Summary:

The derivative of f (x) = tan^-1 (x) is 1/ (1 + x²)