Here's one: find the derivative of (xy)^x = e Thanks!

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Here's one: find the derivative of (xy)^x = e Thanks!

Calculus1
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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This is what I did: I took the natural log to both sides xln(xy)=1 I divided x out of each side ln(xy)=1/x Used properties of logarithms to separate out ln(xy) lnx + lny=1/x lny=-lnx+1/x then I took the derivative to both sides y'/y=-[(1/x^2)+(1/x)] I then multiplied both sides by y, which I just found by using the earlier equation: lny=-lnx+1/x y=e^(-lnx+1/x) y'=-[(1/x^2)+(1/x)][e^(-lnx+1/x)] But I'm sure there's an easier or different way, I just went about it this route since this is where I felt most comfortable.
Very interesting. I asked the question somewhere else and got a different approach but same response. This is actually very helpful to see it done a couple different ways. And thanks for the extra explanations!

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