Q. 143.8( 4 Votes )

Differentiate <sp

Answer :

Let and v = sec–1x


We need to differentiate u with respect to v that is find.


We have



But, cos2θ = cos2θ – sin2θ and sin2θ = 2sinθcosθ.



[ sin2θ + cos2θ = 1]





Dividing the numerator and denominator with, we get








On differentiating u with respect to x, we get





We know and derivative of a constant is 0.




Now, we have v = sec–1x


On differentiating v with respect to x, we get



We know



We have





Thus,


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