Question

differentiate y=tanx-1/secx​

Answer 1

check out the attachment

Answer 2

Answer:

d y / d x = ( sin x + cos x )

Step-by-step explanation:

Given :

y = tan x - 1 / sec x

Diff. w.r.t. x

d y / d x = d ( tan x - 1 / sec x ) / d x

Applying quotient rule :

d y / d x = [ sec x ( tan x - 1 )' - ( tan x - 1 ) ( sec x )' ] / ( sec x )²

d y / d x = [ sec x ( sec² x ) - ( tan x - 1 ) ( sec x tan x ) ] /  ( sec x )²

d y / d x = sec x [ ( sec² x ) - ( tan x - 1 ) (  tan x ) ] /  ( sec x )²

d y / d x = [ ( sec² x ) - ( tan x - 1 ) (  tan x ) ] /  ( sec x )

d y / d x = ( sec² x  -  tan² x + tan x ) / sec x

d y / d x = ( 1 + tan x ) / sec x

d y / d x = ( 1 / sec x + tan x / sec x )

d y / d x = ( cos x + ( cos x × sin x / cos x )

d y / d x = ( cos x + sin x )

Therefore , final answer is ( sin x + cos x )