Question

Find dy/dx if y^3 - xy = -6.

Answer 1

OOohh fun ok

Answer 2

you can use the chain rule on the y terms...
\[\frac{ d }{ dx }=\frac{ d }{ dy }*\frac{ dy }{ dx }\]

Answer 3

for example the first term
\[\large \frac{ d }{ dx }[y^3] = \frac{ d }{ dy }[y^3]\frac{ dy }{ dx }\]

the second term is a product ...

Answer 4

u can take the derivative the normal way just for the derivative of the y it also equals dy/dx and for the x equals dx/dx which is 1 so be don't write it.

Answer 5

Step one: differentiate both sides with respect to x\[\frac{ d }{ dx }y^3-xy=-6\frac{ d }{ dx }\]
\[3y^2\frac{ dy }{ dx }-[y+(\frac{ dy }{ dx })x]=0\]
Clean up everything --> get dy/dx on one side & factor out
\[3y^2\frac{ dy }{ dx }-(\frac{ dy }{ dx })x=y\]
\[\frac{ dy }{ dx }(3y^2-x)=y\]
solve -->

Answer 6

\[\frac{ dy }{ dx }=\frac{ y }{ 3y^2-x }\]