Question

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

Answer 1

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`