Mastering the Chain Rule | Finding the Derivative of Sec(x)

(d/dx) sec(x)

To find the derivative of sec(x), we can use the chain rule

To find the derivative of sec(x), we can use the chain rule.

Let’s start by expressing sec(x) in terms of cos(x).
Recall the identity: sec(x) = 1/cos(x).

Now, to find the derivative, we will apply the chain rule. The chain rule states that if we have a function f(g(x)), then the derivative is given by f'(g(x)) * g'(x).

In this case, f(g(x)) = 1/g(x), where g(x) = cos(x). So, f'(g(x)) = -1/g^2(x) (using the power rule for differentiation).

Now, we need to find g'(x), which is the derivative of cos(x). The derivative of cos(x) is -sin(x).

Putting it all together, we have:
(d/dx) sec(x) = f'(g(x)) * g'(x) = (-1/cos^2(x)) * (-sin(x)) = sin(x)/cos^2(x).

Therefore, the derivative of sec(x) is sin(x)/cos^2(x).

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