Discover the Derivative of Sec(x) Using the Quotient Rule

d/dx sec(x)

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 quotient rule states that if we have a function in the form of f(x) = g(x)/h(x), then its derivative can be found using the formula:

f'(x) = (g'(x) * h(x) – g(x) * h'(x))/[h(x)]^2

For the case of sec(x), we can rewrite sec(x) as 1/cos(x). Therefore, g(x) = 1 and h(x) = cos(x).

Now, let’s find the derivatives of g(x) and h(x):

g'(x) = d/dx(1) = 0 (the derivative of a constant is always zero)

h'(x) = d/dx(cos(x)) = -sin(x) (the derivative of cos(x) is -sin(x))

Using these derivatives, we can apply the quotient rule:

f'(x) = (g'(x) * h(x) – g(x) * h'(x))/[h(x)]^2
= (0 * cos(x) – 1 * (-sin(x)))/(cos(x))^2
= sin(x)/(cos(x))^2

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

More Answers: