The Derivative of Sec(x) with Respect to x: Unraveling the Chain Rule in Calculus

d/dx[secx]

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 composite function, f(g(x)), the derivative of the composite function is given by the product of the derivative of the outer function, f'(g(x)), and the derivative of the inner function, g'(x).

In this case, our outer function is sec(x), and the inner function is x. We know that the derivative of sec(x) is equal to sec(x) * tan(x), as derived in calculus. Therefore, we can say that f'(x) = sec(x) * tan(x).

Now, we need to find the derivative of the inner function, which is x. The derivative of x with respect to x is simply 1.

Using the product rule, the derivative of sec(x) with respect to x is given by:

d/dx[sec(x)] = f'(x) * g'(x)
= (sec(x) * tan(x)) * 1
= sec(x) * tan(x)

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

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