Q. 154.1( 16 Votes )

Find the derivati

Answer :

Let f(x) = cosec x cot x


By product rule


f’(x) = cosec x (cot x)’ + cot x (cosec x)’ ……..(1)


Let f1(x) = cot x, accordingly f1(x + h) = cot (x + h)


By first principle



=


=


=


=


=


(cot x)’ = - cosec2 x ………………..(2)


Let f2(x) = cosec x, accordingly f2(x + h) = cosec (x + h)


By first principle



=


=


=


=


=


= -cosec x cot x


(cosec x)’ = -cosec x cot x ……………….(3)


Putting the value of (2) and (3) in (1)


f’(x) = cosec x (-cosec2 x) + cot x (-cosec x cot x)


= - cosec3 x – cot2 x cosec x


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