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

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Answer 1 · 2017-10-22T22:06:40

Use the Quotient rule

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

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

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

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

$= tanx secx$