Using the Chain Rule to Find the Derivative of Sec(x) with Respect to x

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 composition of functions, the derivative of the composition is the derivative of the outer function multiplied by the derivative of the inner function.

In this case, we can rewrite sec(x) as 1/cos(x). Using the chain rule, we differentiate the outer function (1/x) with respect to the inner function (cos(x)), and then multiply it by the derivative of the inner function.

The derivative of 1/x is -1/x². Now, let’s find the derivative of cos(x). The derivative of cos(x) is -sin(x).

So, differentiating sec(x) using the chain rule, we have:

d/dx(sec(x)) = -1/cos²(x) * (-sin(x))

Simplifying this expression, we get:

d/dx(sec(x)) = sin(x)/cos²(x)

Remember that sin(x)/cos(x) is equal to tan(x), so we can also write the derivative of sec(x) as:

d/dx(sec(x)) = tan(x)/cos(x)

Both of these expressions represent the derivative of sec(x) with respect to x.

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