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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