Question

derivatives y
$= { \tan }^{ - 1} ( \frac{x + 1}{ x - 1} ) + { \tan }^{ - 1} ( \frac{x - 1}{x + 1} ) \\ find \: \frac{dy}{dx}$
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Answer 1

Answer:

Correct option is

A

(1+tan

−1

x)

2

1

.

Let y=

1+tan

−1

x

tan

−1

x

and z=tan

−1

x.

∴y=

1+z

z

=

1+z

z+1−1

=1−

1+z

1

.

∴

dz

dy

=

(1+z)

2

1

=

(1+tan

−1

x)

2

1

.