Differentiate with respect to

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.