# How do you differentiate #y=x^2y-y^2-xy#?

##### 2 Answers

#### Explanation:

Implicit differentiation is used when a function, here

For this, we take differential of both sides of the function

Transposing terms containing

Simplify then differentiate to find:

#(dy)/(dx) = 2x-1# when#y != 0#

Multiply by

#(dy)/(dx) = ((2x-1)y)/(x^2-x-1)#

#### Explanation:

graph{y=x^2y-y^2-xy [-10, 10, -5, 5]}

Notice that all of the terms are divisible by

#1 = x^2-y-x#

with exclusion

We can rearrange this as:

#y = x^2-x-1#

Hence:

#(dy)/(dx) = 2x-1#

with exclusion

What happens in the case

The original equation is satisfied, so its graph consists of the parabola

So to cover the case

So: