# How do you differentiate #(xy)/(x+y)=1#?

##### 3 Answers

#### Explanation:

Using the quotient rule

ie.

giving

We can also rewrite the function from the outset to avoid fractions:

#xy=x+y#

Then we see that the right-hand side will use the quotient rule:

Differentiating gives:

#[d/dxx]y+x[d/dxy]=[d/dxx]+[d/dxy]#

#y+xdy/dx=1+dy/dx#

Grouping the

#xdy/dx-dy/dx=1-y#

Factoring:

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

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

#### Explanation:

We have,