Find the derivatives of the function y defined implicity by

Teddy Dillard 2021-12-17 Answered
Find the derivatives of the function y defined implicity by each of the following equation
x4+y4a2xy=0
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Expert Answer

Thomas Lynn
Answered 2021-12-18 Author has 28 answers
Step 1
Given
x4+y4a2xy=0
Step 2
differentiating wrt "x"
ddx(x4)+ddx(y4)a2ddx(xy)=0
4x3+4y3dydxa2(xdydx+y1)=0
4x3+4y3dydxa2xdydxa2y=0
(4y3a2x)dydx=a2y4x3
dydx=a2y4x24y3a2x

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John Koga
Answered 2021-12-19 Author has 33 answers
Step 1
In implicit differentiation all the differentiation rules are applicable.
Step 2
x4+y4a2xy=0
differentiate both sides wrt x:
ddx(x4+y4a2xy)=ddx(0)
ddx(x4)+ddx(y4)a2ddx(xy)=0
apply chain rule and product rule of differentiation:
4x3+4y3dydxa2(xdydx+ydxdx)=0
4x3+4y3ya2(xy+y)=0
4x3+4y3ya2xya2y=0
y(4y3a2x)=a2y4x3
y=a2y4x34y3a2x
Final answer:
y=a2y4x34y3a2x

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