# 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) / v^{2}

⇒ dy/dx = cos x.cos x - sin x(-sin x) / cos^{2 }x

⇒ dy/dx = (cos^{2 }x + sin^{2 }x) / cos^{2 }x

⇒ dy/dx = 1 / cos^{2 }x

⇒ dy/dx = sec^{2}(x)

Thus, the derivative of y = tan(x) is sec^{2}(x).

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

**Summary:**

The derivative of y = tan(x) is sec^{2}(x).

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