Use implicit differentiation to find
d
y
d
x
\displaystyle \frac{{\left.{d}{y}\right.}}{{{\left.{d}{x}\right.}}}
d
x
d
y
.
y
2
+
8
x
3
=
3
y
−
6
x
2
\displaystyle {y}^{{2}}+{8}{x}^{{3}}={3}{y}-{6}{x}^{{2}}
y
2
+
8
x
3
=
3
y
−
6
x
2
d
y
d
x
=
\displaystyle \frac{{\left.{d}{y}\right.}}{{{\left.{d}{x}\right.}}}=
d
x
d
y
=
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