Using implicit differentiation, what is the derivative of 5x^2y+ 2x^3y^5=2xy?

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Using implicit differentiation, what is the derivative of 5x^2y+ 2x^3y^5=2xy?

2007-01-19 08:49:26 · 2 answers · asked by Calvin N 1 in Science & Mathematics ➔ Mathematics

2 answers

10xy + 5x²y' + 6x²y^5 + 10x³y⁴y' = 2y + 2xy'

5x²y' - 2xy' + 10x³y⁴y' = 2y - 10xy - 6x²y^5

y'(5x² - 2x + 10x³y⁴) = 2y - 10xy - 6x²y^5

y' = (2y - 10xy - 6x²y^5)/(5x² - 2x + 10x³y⁴)

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Not sure why I got a thumbs-down. I checked it and re-checked it. I did assume you wanted y' not x'...?

2007-01-19 08:55:40 · answer #1 · answered by Jim Burnell 6 · 0⤊ 1⤋

Jim's answer looks right on to me.

2007-01-19 17:18:18 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋