## ddx secx

### 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. The derivative of sec(x) is given by:

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

Here’s a step-by-step explanation of how we get this result:

First, we can rewrite sec(x) as 1/cos(x).

d/dx(sec(x)) = d/dx(1/cos(x))

Next, we can use the quotient rule to differentiate 1/cos(x). The quotient rule states that for a function u(x)/v(x), the derivative is given by:

d/dx(u(x)/v(x)) = (v(x) * du(x)/dx – u(x) * dv(x)/dx) / (v(x))^2

In our case, u(x) = 1 and v(x) = cos(x). So let’s differentiate 1 and cos(x) separately:

du(x)/dx = 0 (since 1 is a constant)

dv(x)/dx = -sin(x) (since the derivative of cos(x) is -sin(x))

By substituting u(x), v(x), du(x)/dx, and dv(x)/dx into the quotient rule formula, we get:

d/dx(1/cos(x)) = (cos(x) * 0 – 1 * (-sin(x))) / (cos(x))^2

= sin(x) / (cos(x))^2

Now, we can simplify sin(x) / (cos(x))^2 using trigonometric identities. Since sin(x)/cos(x) is equal to tan(x), we have:

d/dx(sec(x)) = sin(x) / (cos(x))^2

= tan(x) / (cos(x))^2

= tan(x) * sec(x)

So, the derivative of sec(x) is sec(x) * tan(x).

## More Answers:

Understanding the Chain Rule: Derivative of cos(x) with Respect to x is -sin(x)How to Find the Derivative of the Tangent Function: Step-by-Step Guide with Quotient Rule & Simplification

Derivative of cot(x): Exploring Quotient Rule & Alternative Expressions