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Question
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `(tanx - 1)/secx`
Solution
y = `(tanx - 1)/secx`
`("d"y)/("d"x) = (secx(sec^2x - 0) - (tan x - )secx tanx)/(sec x)^2`
`("d"y)/("d"x) = (secx[sec^2x - (tan x - 1) tanx])/(sec^2x)`
= `([sec^3x - tan^2xx + tanx])/secx`
= `((1 + tanx))/secx`
= `cos x (1 + sinx/cosx)`
`("d"y)/("d"x)` = cos x + sin x
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