Calculating the Derivative of sec(x) | The Chain Rule Approach

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.

Recall that the derivative of sec(x) is the derivative of 1/cos(x).

Using the quotient rule, we have:

(d/dx) (1/cos(x)) = (cos(x)(d/dx)(1) – 1(d/dx)(cos(x))) / cos^2(x)

The derivative of 1 is 0, and the derivative of cos(x) is -sin(x). Substituting these values, we get:

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

Since sec(x) is equal to 1/cos(x), we can rewrite the derivative as:

= sin(x) * sec(x)^2

Therefore, the derivative of sec(x) is sin(x) times the square of sec(x), which can also be written as sec(x) * tan(x).

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