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Question

10. y = tan-i |

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Solution

The given equation is,

y= tan 1 ( 3x x 3 13 x 2 )

Substitute x=tanθ.

y= tan 1 ( 3x x 3 13 x 2 ) = tan 1 ( 3( tanθ ) tan 3 θ 13 tan 2 θ ) = tan 1 ( tan3θ ) =3θ

Substitute θ= tan 1 x in the above equation.

y=3 tan 1 x

Differentiate the above equation with respect to x.

y=3 tan 1 x dy dx =3 d dx ( tan 1 x ) = 3 1+ x 2

Thus, the derivative of y= tan 1 ( 3x x 3 13 x 2 ) is dy dx = 3 1+ x 2 .


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