William W. answered • 07/31/24
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To get the slope, take the derivative. Since the x's and y's are mixed together, we can use implicit differentiation: Replacing the radicals with a fractional exponent we get:
(3x + 3y)1/2 + (5xy)1/2 = 12.328542387371
The chain rule must be applied as well as the product rule for the 2nd term:
1/2(3x + 3y)-1/2(3 + 3y') + 1/2(5xy)-1/2(5y + 5xy') = 0
Plugging in the values of x and y and doing a lot of arithmetic, we get y' = -(192 + 3√35)/262
William W.
It's possible they used a decimal equivalent y' = -0.800565799 or some rounded off version of that. I chose to use the exact value. You can use desmos to double check the answer. It shows it being correct.
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08/03/24
Novalee S.
That did not end up being correct...08/01/24