Understanding the Derivative of Sec(x): Step-by-Step Guide & Formula Revealed

Derivitive of sec(x)

To find the derivative of sec(x), we can use the quotient rule

To find the derivative of sec(x), we can use the quotient rule. However, it is more convenient to derive it from the identity sec(x) = 1/cos(x).

Let’s start by finding the derivative of cos(x). We know that the derivative of cos(x) is -sin(x).

Now, using the quotient rule, we can find the derivative of sec(x):

d/dx [sec(x)] = d/dx [1/cos(x)]

= [0 * cos(x) – 1 * (-sin(x))] / (cos(x))^2

= sin(x) / (cos(x))^2

= sin(x) / cos^2(x)

= sin(x) * (1/cos^2(x))

= sin(x)/cos^2(x)

Recall that sin(x) / cos^2(x) is the same as sec(x) * tan(x).

Therefore, the derivative of sec(x) is sec(x) * tan(x).

In summary, the derivative of sec(x) is sec(x) * tan(x).

More Answers:

Understanding Rolle’s Theorem: Finding Zero Points in Functions’ Derivatives within a Given Interval
The Quotient Rule: Finding the Derivative of tan(x)
Understanding the Derivative of cot(x) and How to Calculate it Using the Quotient Rule.

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