Derivative of sec(x) using the quotient rule and the derivative of sin(x)

derivative of sec(x)

To find the derivative of sec(x), we can use the quotient rule and the derivative of sin(x)

To find the derivative of sec(x), we can use the quotient rule and the derivative of sin(x).

Recall that sec(x) is equal to 1/cos(x). Now, let’s differentiate it step by step:

First, we need to determine the derivative of the numerator and the denominator separately.

The derivative of 1 is 0, as it is a constant.

Now, let’s find the derivative of cos(x).

The derivative of cos(x) is -sin(x), as the derivative of cos(x) is equal to the negative of the derivative of sin(x).

So, applying the quotient rule, we have:

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

Simplifying this expression, we get:

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

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

Therefore, the derivative of sec(x) is given by sin(x) / (cos(x))^2.

More Answers: