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Question
Find the derivatives of the following:
If cos(xy) = x, show that `(-(1 + ysin(xy)))/(xsiny)`
Solution
cos (xy) = x
Differentiating with respect to x
`- sin (xy) [x * ("d"y)/("d"x) + y * 1]` = 1
`- x sin (xy) ("d"y)/("d"x) - y sin (xy)` = 1
`- sin (xy) ("d"y)/("d"x) = 1 + y sin (xy)`
`("d"y)/("d"x) = -((1 y sin(xy)))/(x sin (xy))`
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