Question

Differentiate the following. w.r.t. X :................tan^-1( SEC X+TAN X)

Answer 1

Let us assume that

U=secx + tanx

X=tan^-1(u)
As we know that,

Tan^-1x=1/1+x^2

Apply the value of u in the x term


=1/1+(sec x +tan x)^2

=1/1+(sec^2x+tan^2x+2 secx tanx)

=1/1+(1+2sec x tan x)

=1/2+2sec x tan x)....

Please check the answer...
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Answer 2

y =tan^-(secx + tanx)
differentiate wrt x

dy/dx = 1/{ 1+( secx+tanx)² } { secx.tanx+sec²x}

= 1/( 1+ tan²x + sec² + 2secx.tanx} { secx(tanx + secx )}

=1/(2sec²x + 2secx.tanx } { secx( secx+tanx)}

=secx(secx +tanx)/2secx( secx +tanx)

=1/2