Math Problem Statement

differentiate tan(x)

Solution

To differentiate tan(x)\tan(x), we use the fact that:

ddx(tan(x))=sec2(x)\frac{d}{dx} \left( \tan(x) \right) = \sec^2(x)

So, the derivative of tan(x)\tan(x) is sec2(x)\sec^2(x).

Let me know if you'd like more details or have any questions!

Here are 5 related questions:

  1. How would you differentiate cot(x)\cot(x)?
  2. What is the derivative of sin(x)\sin(x)?
  3. How do you differentiate trigonometric functions involving composite functions, like tan(2x)\tan(2x)?
  4. What is the integral of sec2(x)\sec^2(x)?
  5. How would you differentiate tan1(x)\tan^{-1}(x)?

Tip: Keep in mind that sec2(x)\sec^2(x) is the reciprocal of cos2(x)\cos^2(x), which often makes simplifying trig derivatives easier!

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Math Problem Analysis

Mathematical Concepts

Differentiation
Trigonometry
Secant and Tangent Functions

Formulas

d/dx(tan(x)) = sec^2(x)

Theorems

Derivative of Tangent Function

Suitable Grade Level

Grades 11-12