How To Find The Derivative Of Sec(X) And Simplify The Result

d/dx secx

secxtanx

To find the derivative of sec(x), we’ll need to use the chain rule and the derivative of the cosine function. The chain rule tells us that if we have a function that can be written as f(g(x)), then its derivative is f'(g(x)) * g'(x).

Here, we can write sec(x) as 1/cos(x).

Taking the derivative of 1/cos(x), we get

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

Using the fact that -sin(x) = sin(-x), we can rewrite this as

d/dx(1/cos(x)) = sin(x)/cos(x)^2

But since sin(x)/cos(x) = tan(x), we can also write

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

Finally, using the fact that 1/cos(x) = sec(x), we get

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

Therefore, the derivative of sec(x) is tan(x)/cos(x).

More Answers: