Derivative of Tangent Function: A Step-by-Step Guide and Formula

Dx {tan x}=?

To find the derivative of the tangent function, Dx {tan x}, we can use the quotient rule

To find the derivative of the tangent function, Dx {tan x}, we can use the quotient rule.

The tangent function can be written as tan x = sin x / cos x.

Let’s differentiate sin x and cos x separately first:

Dx {sin x} = cos x
Dx {cos x} = -sin x

Now, we can apply the quotient rule:

Dx {tan x} = (Dx {sin x} * cos x – sin x * Dx {cos x}) / (cos x)^2

Substituting the values we found earlier:

Dx {tan x} = (cos x * cos x – sin x * (-sin x)) / (cos x)^2
= (cos^2 x + sin^2 x) / (cos x)^2
= 1 / (cos x)^2

Therefore, the derivative of the tangent function is Dx {tan x} = 1 / (cos x)^2.

More Answers:

The Power Rule for Finding the Derivative of the Exponential Function e^x
Derivative of f(x) = a^x with Respect to x Using Logarithmic Differentiation
Understanding and Applying the Quotient Rule in Calculus Differentiation

Error 403 The request cannot be completed because you have exceeded your quota. : quotaExceeded

Share:

Recent Posts

Mathematics in Cancer Treatment

How Mathematics is Transforming Cancer Treatment Mathematics plays an increasingly vital role in the fight against cancer mesothelioma. From optimizing drug delivery systems to personalizing

Read More »