How to Find the Derivative of the Function sec(x) with Respect to x: Applying the Chain Rule

𝑑/𝑑𝑥[sec 𝑥]

To find the derivative of the function sec(x) with respect to x, we can apply the chain rule

To find the derivative of the function sec(x) with respect to x, we can apply the chain rule.

The chain rule states that if we have a composite function, f(g(x)), then the derivative of this function is given by the product of the derivative of the outer function with the derivative of the inner function.

In this case, the outer function is sec(x), and the inner function is x.

The derivative of the outer function sec(x) is given by the formula -sec(x)tan(x).

To find the derivative of the inner function, which is simply x, we can use the power rule. The power rule states that if we have a function of the form x^n, then the derivative with respect to x is given by n*x^(n-1).

Since the power of x is 1, the derivative of x with respect to x is simply 1.

Now, we can apply the chain rule:

𝑑/𝑑𝑥[sec 𝑥] = 𝑑/𝑑𝑥[sec(x)] * 𝑑/𝑑𝑥[x]

= -sec(x)tan(x) * 1

= -sec(x)tan(x)

So, the derivative of sec(x) with respect to x is -sec(x)tan(x).

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