Q. 94.5( 2 Votes )

Differentiate with respect to

Answer :


Given : Let u = and v =


To differentiate : with respect to


Formula used : n.




The CHAIN RULE states that the derivative of f(g(x)) is f’(g(x)).g’(x)


Let u = and v =


Put x = cot θ or θ = in u


= =


= = =


=


We know that 1 - = - 2 and =


1 - =


Substituting the above values in ,we get


= =


=


Dividing by cos on numerator and denominator,we get


= = =


= =


Differentiating u with respect to x


= =


=


v =


Put x = tanθ


V = = = = =


V = = = = 2θ = 2


V = = 2


Differentiating v with respect to x


=


=


= =


=


Ans.


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