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

Textbook Question

Chapter 2, 2.5 - Problem 28 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

`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))`

``

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kandukurimaths's profile pic

kandukurimaths | Student, Graduate | (Level 1) Honors

Posted on

 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)`

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