Finding the Derivative of the Secant Function | Explained Step-by-Step with Quotient Rule

Derivative of Sec

The derivative of the secant function can be found using the quotient rule, as follows:

Let y = sec(x)
Taking the derivative of y with respect to x, we get:

dy/dx = d/dx(sec(x))

Using the quotient rule, the derivative of sec(x) is given by:

dy/dx = (sec(x) * tan(x) * dx/dx – sec(x)^2 * sin(x))/(sec(x))^2

Simplifying, we have:

dy/dx = tan(x) / sec(x)

We know that sec(x) = 1/cos(x), and substituting this, we get:

dy/dx = tan(x) * cos(x)

Therefore, the derivative of sec(x) is equal to the product of the tangent function and the cosine function, i

The derivative of the secant function can be found using the quotient rule, as follows:

Let y = sec(x)
Taking the derivative of y with respect to x, we get:

dy/dx = d/dx(sec(x))

Using the quotient rule, the derivative of sec(x) is given by:

dy/dx = (sec(x) * tan(x) * dx/dx – sec(x)^2 * sin(x))/(sec(x))^2

Simplifying, we have:

dy/dx = tan(x) / sec(x)

We know that sec(x) = 1/cos(x), and substituting this, we get:

dy/dx = tan(x) * cos(x)

Therefore, the derivative of sec(x) is equal to the product of the tangent function and the cosine function, i.e., dy/dx = tan(x) * cos(x).

In summary, the derivative of the secant function is given by dy/dx = tan(x) * cos(x).

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