How do you find $dy/dx$ by implicit differentiation of $x^3+y^3=8$ ?

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Answer 1 · 2017-02-13T01:18:37

$dy/dx=-x^2/y^2$

We have:

$x^3+y^3=8$

Differentiate wrt $x$ ; then Apply the chain rule (implicit differentiation):

$3x^2 + d/dxy^3=0$
$:. 3x^2 + dy/dxd/dyy^3=0$
$:. 3x^2 + dy/dx(3y^2)=0$
$:. x^2 + y^2dy/dx=0$
$:. dy/dx=-x^2/y^2$

How do you find dy/dxdy/dx by implicit differentiation of x^3+y^3=8x^3+y^3=8?