Question

How do you implicitly differentiate −1=xy+cot2(xy)?

Answer 1

How do you implicitly differentiate −1=xy+cot2(xy)?

Ans= -1=xy + cot 2(xy)

diff wrt x 0 = x. dy/dx + y. 1 + [- cosec ^2 (xy) .( x dy/dx + y) ]

= x. dy/dx + y - cosec ^2 (xy). x dy/dx +y

= x. dy/dx - cosec^2 (xy ) .x dy/dx + 2y

= dy/dx [ x - cosec^2 (xy) x ] + 2y.

= dy/dx .x ( 1- cosec^2 (xy ) +2y

= dy/ dx . x . cot^2 (xy) + 2y

therefor dy/dx = -( 2 y + x cot ^ 2 (xy )

dy/dx = -[2y + x cot ^ 2 (xy) ]

thanks