Find dy/dx.
x^2 + xy - y^3 = xy^2
can someone help me out with this one, im not sure exactly where to put dy/dx when differentiating. thanks
mathlete
Remember as you do these that y is a function of x, so when you have to differentiate y at any point, the result will be - simply the derivative of y with respect to x.
Take the derivative with respect to x on both sides.
The derivative of .
To find the derivative of xy, you need to use the product rule, and you get:
.
The derivative of .
The derivative of again requires the product rule, giving:
.
Put it all together and you get:
.
Get all the dy/dx on one side, everything else on the other. Factor out dy/dx from all the terms that have it, then divide to get dy/dx by itself.