Find dy/dx by implicit differentiation. 7 cos x sin y = 1     y'=?

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Find `(dy)/(dx)` if `7cosxsiny=1` :

Differentiate both sides with respect to `x` :


Use the product rule: `d/(dx)[u*v]=u'v+uv'` :


`=7[-sinxsiny+cosxcosy(dy)/(dx)]` using the chain rule on `d/(dx)siny`

So the derivative of the left hand side is `-7sinxsiny+7cosxcosy(dy)/(dx)` and teh derivative of the right hand side is 0.






Given `7cosxsiny=1` then `(dy)/(dx)=tanxtany`




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