What is the derivative of y = tan(x)?

Solution:

To find the derivative of y = tan x, we will use the quotient rule.

Given, y = tan x.

Let u = sin x and v = cos x

On applying quotient rule on y = sin x / cos x, we get,

∵ dy/dx = (v.du/dx - u.dv/dx) / v²

⇒ dy/dx = cos x.cos x - sin x(-sin x) / cos² x

⇒ dy/dx = (cos² x + sin² x) / cos² x 

⇒ dy/dx = 1 / cos² x

⇒ dy/dx = sec²(x)

Thus, the derivative of y = tan(x) is sec²(x).

What is the derivative of y = tan(x)?

Summary:

The derivative of y = tan(x) is sec²(x).