Derivative of sec(x) | Using Chain Rule to Find the Derivative of the Secant Function

d/dx[sec(x)]

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 chain rule states that if we have a composite function f(g(x)), the derivative of this function with respect to x is given by f'(g(x)) * g'(x).

In the case of sec(x), we can rewrite it as 1/cos(x), since sec(x) is the reciprocal of cos(x).

Now let’s find the derivative using the chain rule.

First, let’s find the derivative of cos(x):

d/dx[cos(x)] = -sin(x)

Next, we can find the derivative of sec(x) using the chain rule:

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

Simplifying this expression, we have:

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

Alternatively, we can write it as:

d/dx[sec(x)] = tan(x) * sec(x)

So, the derivative of sec(x) with respect to x is sin(x)/cos^2(x) or equivalently, tan(x) * sec(x).

Note: It is important to simplify the result as much as possible, but the answer can also be left in the form of tan(x) * sec(x).

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