d/dx [secx]
secxtanx
To determine the derivative of the secant of x with respect to x, we can use the quotient rule.
Recall that sec x is defined as 1/cos x. Using the quotient rule, we have:
d/dx [sec x]
= d/dx [1/cos x]
= (-1/cos^2 x) * d/dx [cos x]
To evaluate the derivative of cos x, we can use the chain rule:
d/dx [cos x] = -sin x
Substituting this into the original equation, we obtain:
d/dx [sec x]
= (-1/cos^2 x) * (-sin x)
= sin x/cos^2 x
Recall that sin x/cos x is equal to tan x. Therefore, we can simplify the expression as:
d/dx [sec x] = tan x * sec x
Therefore, the derivative of sec x with respect to x is equal to: tan x * sec x.
More Answers:
[next_post_link]