Mastering Calculus: How To Find D Tan X Using Basic Differentiation Rules

d tan x

sec^2 x

The expression d tan x is the derivative of the tangent function with respect to the variable x. We can find this derivative using the basic differentiation rules of calculus as follows:

First, we can write tangent as a ratio of sine and cosine:

tan x = sin x / cos x

Then, we can use the quotient rule to differentiate this expression:

(d/dx) tan x = (d/dx) [sin x / cos x]
= [cos x (d/dx) sin x – sin x (d/dx) cos x] / cos^2 x

Now, we need to find the derivatives of sine and cosine:

(d/dx) sin x = cos x
(d/dx) cos x = -sin x

Substituting these values into our expression, we get:

(d/dx) tan x = [cos x (cos x) – sin x (-sin x)] / cos^2 x
= (cos^2 x + sin^2 x) / cos^2 x
= 1 / cos^2 x

Therefore,

d tan x = 1 / cos^2 x

More Answers: