If y=log(xy). Find dy/dx |

We need to differentiate an implicit function. Implicit differentiation is very similar to regular differentiation. We just have to bear in mind that  is a function if   Therefore, if we need to differentiate a function of  we will proceed as follows:

You can see more examples in the link below.

We differentiate the whole equation (both left and right side).

In the line above we have applied...

We need to differentiate an implicit function. Implicit differentiation is very similar to regular differentiation. We just have to bear in mind that  is a function if   Therefore, if we need to differentiate a function of  we will proceed as follows:

You can see more examples in the link below.

We differentiate the whole equation (both left and right side).

In the line above we have applied the chain rule because  is a composite function. On top of that we have applied product rule for  to get expression in the brackets.

Factor the left side.

 <-- Solution            

We could also put  instead of  but that wouldn't make the solution any simpler.