`xcos(y) = 1, (2,(pi/3))` Find `dy/dx` by implicit differentiation and evaluate the derivative at the given point.

Expert Answers
hkj1385 eNotes educator| Certified Educator

`xcos(y) = 1`

` `

Differentiating both sides w.r.t 'x' we get

`-xsin(y)*(dy/dx) + cos(y) = 0`

`or, dy/dx = cos(y)/{xsin(y)}`

``Now, dy/dx at (2,pi/3) is :-

`dy/dx = cos(pi/3)/{2*sin(pi/3)}`

`or, dy/dx = 1/(2sqrt(3))`

``

kandukurimaths | Student

 at (2,`pi` /3)

cos(y)=1/x

derivative both side with respect to x

-sin(y)dy/dx=-1/x^2

dy/dx=1/2*`sqrt(3)`