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Question
Find `dy/dx` in the following:
sin2 x + cos2 y = 1
Solution
sin2 x + cos2 y = 1
On differentiating with respect to both x and y,
`d/dx sin^2 x + d/dx cos^2 y = (d(1))/dx`
`=> 2 sin x d/dx sin x + 2 cos y d/dx cos y = 0`
`=> 2 sin x cos x + 2 cos y (- sin y) dy/dx = 0`
`=> 2 sin x cos x - 2 cos y sin y dy/dx = 0`
`=> sin 2x - sin 2 y dy/dx = 0`
`=> dy/dx = (sin 2x) /(sin 2 y)`
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