How do you find \frac{d^2y}{dx^2} by implicit differentiation where x^2y+xy^2=3x

Donald Johnson 2021-12-15 Answered
How do you find d2ydx2 by implicit differentiation where x2y+xy2=3x
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Stella Calderon
Answered 2021-12-16 Author has 35 answers
Differentiating
x2y+xy2=3x
with respect to x we get
2xy+x2y+y2+2xyy=3
So we get
y=3y22xyx2+2xy
for the second derivative we obtain
y=(2yy2y2xy)(x+2xy)(3y22xy)(2x+2y+2xy)(x2+2xy)2
Now plug the result for y' in this equation!
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William Appel
Answered 2021-12-17 Author has 44 answers

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