How to Find the Derivative of Sec(x) Using the Quotient Rule and Chain Rule

Derivative of secx

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

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

The secant function is defined as sec(x) = 1/cos(x).

Using the quotient rule, the derivative of sec(x) can be calculated as follows:

d/dx (sec(x)) = (cos(x) * d/dx(1)) – (1 * d/dx(cos(x))) / (cos(x))^2

Now, d/dx(1) is equal to 0, since the derivative of a constant is always 0.

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

To find d/dx(cos(x)), we can use the chain rule.
The derivative of cos(x) with respect to x is equal to -sin(x).

Therefore,

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

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

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

= sin(x) * sec^2(x)

So, the derivative of sec(x) is sin(x) * sec^2(x).

More Answers:

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