I did this three times, and always come up with utter nonsense.(adsbygoogle = window.adsbygoogle || []).push({});

What is the derivative of 4x(16-x^2)^0.5?

(Root of (16 minus x-squared) by 4x.) What are its zilches? How did you calculate that?

This derivative is part of the solution to this problem: "What are the dimentions of the largest rectangle (by area) inscribable in a circle with radius 4?"

I drew the circle and the square (see attachment), divided the square into four parts, drew a diagonal through one, and called it a hypotenuse, which is equal to 4. X and y are the sides of the mini squares. A = 4xy (since there are 4 mini-squares). Then I used Pythagoras to come up with that equation above. But I can't differentiate it now...

The final answer is supposed to be 32 square units.

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# What is the derivative of 4x(16-x^2)^0.5?

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