Understanding the Derivative of Sec(x): Step-by-Step Guide for Calculating and Simplifying

d/dx(secx)

To find the derivative of sec(x) with respect to x, we can use the chain rule

To find the derivative of sec(x) with respect to x, we can use the chain rule.

The derivative of sec(x) can be found by writing it as 1/cos(x), since sec(x) is the reciprocal of cos(x).

Now, let’s apply the chain rule:

d/dx(1/cos(x)) = -1/cos(x)^2 * d/dx(cos(x))

The derivative of cos(x) is equal to -sin(x). Therefore:

d/dx(sec(x)) = -1/cos(x)^2 * (-sin(x))

Simplifying this expression gives:

d/dx(sec(x)) = sin(x)/cos(x)^2

Since sin(x) divided by cos(x) is equal to tan(x), we could also write the derivative of sec(x) as:

d/dx(sec(x)) = tan(x)/cos(x)

Either of these expressions is the correct derivative of sec(x) with respect to x.

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