Hw do you prove that the d/dx (secx) = sec x tan x ?

1 Answer
Oct 22, 2017

Use the Quotient rule

Explanation:

STEP 1:
sec x = 1 / cos x

STEP 2:
Use the quotient rule to find the derivative of Sec x = 1 / cos x

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

STEP 3:
Simplify

= ((0) cosx - (-sinx)) / (cosx)^2

= (sinx) /((cosx)(cosx))

= (sinx / cos x ) (1 / cosx)

= tanx secx