(d/dx) sec(x)
To find the derivative of sec(x), also known as the derivative of the secant function, we can use the chain rule
To find the derivative of sec(x), also known as the derivative of the secant function, we can use the chain rule.
The chain rule states that if y = f(g(x)), then the derivative of y with respect to x (dy/dx) is given by dy/dx = f'(g(x)) * g'(x).
In this case, we can rewrite sec(x) as y = 1/cos(x). Let’s find dy/dx by applying the chain rule.
First, let’s find the derivative of g(x) = x, which is g'(x) = 1.
Next, let’s find the derivative of f(u) = 1/u, where u = cos(x). Using the power rule, we have f'(u) = -1/u^2.
Now, we can apply the chain rule: dy/dx = f'(g(x)) * g'(x).
Substituting in the values:
dy/dx = (-1/(cos(x))^2) * 1
dy/dx = -1/(cos(x))^2
Therefore, the derivative of sec(x) is -1/(cos(x))^2.
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