Q. 11 E3.8( 19 Votes )

Find the derivati

Answer :

Let f(x) = 3 cot x + 5 cosec x


f’(x) = 3 (cot x)’ + 5 (cosec x)’


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


So, f’(x) = 3 (cot x)’ + 5 (cosec x)’


Putting (cot x)’ and (cosec x)’ in f’(x)


f’(x) = 3 × (-cosec2 x) + 5 × (-cosec x cot x)


f’(x) = -3cosec2 x – 5cosec x cot x


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