Differentiate with respect respect to w 4r^2=l^2+w^2

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Differentiate with respect respect to w 4r^2=l^2+w^2

Mathematics
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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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I understand the right side will be \[ = 2l \frac{ dl }{ dw }+2w\] the left side shown to be zero in my model answers.. plz help
is it given that L is a function of w, is r a constant?

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im trying to figure out the maximum area of a rectangle inside a circle. so the above equation was used to express the radius
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now that i think of it, yes r is a constant i guess becuase i am after the maximum l and w in order to get the maximum area...
yes radius is a constant in this problem, length and width are variables . that is why you have 0 when you take derivative of r^2
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***im trying to figure out the maximum area of a rectangle inside a circle*** if you allowed "r" to vary, then you are changing the circle (i.e. its size) and the problem makes no sense: what is the biggest rectangle I can put in a circle, if I am allowed to change the size of the circle? It makes more sense to ask the question: what is the biggest rectangle I can put in a circle that has a *fixed radius* r? in other words, we should treat r as a constant in this problem.
Thank you!

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