Finding the Derivative of Sec x: Step-by-Step Guide with Chain Rule Application

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 function of the form f(g(x)), then its derivative is given by f'(g(x)) multiplied by g'(x).

In this case, f(x) = sec x and g(x) = x. Applying the chain rule, we have:

d/dx [sec x] = f'(g(x)) * g'(x)

The derivative of sec x can be found by using the derivative of secant x, which is -sec x * tan x. Therefore, f'(x) = -sec x * tan x.

Since g(x) = x, g'(x) = 1.

Now, we can substitute these values back into the chain rule formula:

d/dx [sec x] = (-sec x * tan x) * (1)

Simplifying, we have:

d/dx [sec x] = -sec x * tan x

Therefore, the derivative of sec x with respect to x is -sec x * tan x.

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