When I check my answer using the some website, I get a result I can't agree with. So I'd like to hear your opinion :)Asked: use implicit differentiation to differentiate sin ⁡ ( x y ).My take on the matter:Using the chain rule: d d x sin ⁡ ( x y ) = cos ⁡ ( x y ) d d x x y, then using the product rule on latter factor we get: d d x x y = y + x d y d x Hence: d d x sin ⁡ ( x y ) = y cos ⁡ ( x y ) + x cos ⁡ ( x y ) d y d x .Is this correct?

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When I check my answer using the some website, I get a result I can&#039;t agree with. So I&#039;d like to hear your opinion :)Asked: use implicit differentiation to differentiate   sin  ⁡  (  x  y  ).My take on the matter:Using the chain rule:       d          d      x        sin  ⁡  (  x  y  ) =   cos  ⁡  (  x  y  )      d          d      x        x  y, then using the product rule on latter factor we get:       d          d      x        x  y  =  y  +  x            d      y              d      x      Hence:       d          d      x        sin  ⁡  (  x  y  )  =  y  cos  ⁡  (  x  y  )  +  x  cos  ⁡  (  x  y  )            d      y              d      x      .Is this correct?

luthersavage6lm · Accepted Answer

Depending on how you enteblack it into WolframAlpha, it is most likely partial differentiating, meaning it considers   x and   y to be independent variables (specifically,             ∂      y              ∂      x        =  0). This is why WA&#039;s result is different from yours. If you want WA to interpret   y as a function of   x, you have to write   y(  x), not just   y when you enter y into the expression.Your results looks fine as it is.

Leanna Jennings · Accepted Answer

I think you have the function   f  (  x  )  =  sin  ⁡  (  x  y  (  x  )  ), where   y is a differentiable function of   x.In this case your answer is correct.If you have the function   g  (  x  ,  y  )  =  sin  ⁡  (  x  y  ) of two variables, then website computed the partial derivative       g    x    .

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