Q:
# What Is the Derivative of Tan (x)?

**The derivative of the tangent of x is the secant squared of x.** This is proven using the derivative of sine, the derivative of cosine and the quotient rule.

The first step in determining the tangent of x is to write it in terms of sine and cosine. The quotient identities indicate this equals the sine of x divided by the cosine of x.

The derivative of the tangent of x therefore equals the derivative of the sine of x divided by the cosine of x. This is obtained using the quotient rule. It equals the sum of the cosine squared of x plus the sine squared of x divided by the cosine squared of x.

The Pythagorean identity of sine and cosine allows this to be expressed as one divided by the cosine squared of x. It is then simplified and written as the secant squared of x.

Learn more about Trigonometry-
Q:
## What Is the Way to Evaluate Sin(arc-Tan X)?

A: Evaluating sin(arc-tan x) is a simple process that involves two steps: using a right-angled triangle to label the two sides and the angle in question, whic... Full Answer >Filed Under: -
Q:
## How Do You Use a Unit Circle With Tangent Chart?

A: A unit circle can help solve values for the tangent of angles 30 degrees, 45 degrees and 60 degrees. Tan (θ) = x/y, sin (θ) = y and cos (θ) = x. By substit... Full Answer >Filed Under: -
Q:
## What Is a Tangent Line Approximation?

A: Tangent line approximation is used in calculus to approximate the values of a function based on its tangent. Tangent line approximation can be used because... Full Answer >Filed Under: -
Q:
## How Do You Find the Tangent?

A: Find the tangent by dividing the length of the opposite side of a right triangle by the length of its adjacent side. The result of this equation is the tan... Full Answer >Filed Under: