Question

How do you use implicit differentiation to find dy/dx given `xcosy=1`?

Answer 1

Please see the explanation.

Explanation:

`(d(xcos(y)))/dx = (d(1))/dx`

Use the product rule on the left; the right side is 0:

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

`xsin(y)dy/dx = cos(y)`

`dy/dx = cos(y)/(xsin(y))`

`dy/dx = cot(y)/x`