Which of the following functions are derivable and why???

I) tan x

II) cosec

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Solution

Using the quotient rule it is easy to obtain an expression for the derivative of tangent:
(tanx)′=(sinx/cosx)′
=(sinx)′cosx−sinx(cosx)′/cos^2x
=cosx⋅cosx−sinx⋅(−sinx)/cos^2x
=cos^2x+sin^2x/cos^2x=1/cos^2x.
Similarly, we find the derivatives of cosecant:

(cosecx)′=(1/sinx)′
=−1/sin^2x⋅(sinx)′
=−cosx/sin^2x
=−cosx/sinx⋅1/sinx
=−cotx.cscx.

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Which of the following functions are derivable and why??? I) tan x II) cosec

Which of the following functions are derivable and why???

I) tan x

II) cosec