Q. 5 B5.0( 1 Vote )

Differentiate <sp

Answer :

Let and.


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


We have



By substituting 2x = cos θ, we have




[ sin2θ + cos2θ = 1]


u = sin–1(2 cos θ sin θ)


u = sin–1(sin2θ)


Given


However, 2x = cos θ






Hence, u = sin–1(sin 2θ) = 2θ.


u = 2cos–1(2x)


On differentiating u with respect to x, we get




We know and derivative of a constant is 0.






However,




In part (i), we found


We have





Thus,


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