Part 1/4:
Understanding the Derivative of Tan X Using the Quotient Rule
Calculating the derivative of the tangent function might be intimidating for some, but by using the quotient rule, the process becomes much simpler. In this article, we will break down the steps to derive the derivative of ( \tan(x) ) using foundational concepts from trigonometry and calculus.
Introduction to Tangent Function
To start, let's recognize that the function ( f(x) = \tan(x) ) can be expressed in terms of sine and cosine:
[
f(x) = \tan(x) = \frac{\sin(x)}{\cos(x)}
]