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7.3.37-eg - ln x e y d dx(ln x cos y dy dx = e y dy...

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Example Find dy dx if sin( y ) = e y ln( x ). Since we cannot solve explicitly for y in terms of x (note that y = y ( x )), we use implicit differentiation. First differentiate both sides of the equation with respect to x : d dx (sin( y )) = d dx ( e y ln( x )) , cos( y ) · dy dx = d dx ( e y
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Unformatted text preview: ) · ln( x ) + e y · d dx (ln( x )) cos( y ) · dy dx = e y · dy dx · ln( x ) + e y 1 x , Then solve for dy dx : dy dx (cos( y )-e y ln( x )) = e y x dy dx = e y x (cos( y )-e y ln( x ))...
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