# What is the implicit derivative of #25=sin(xy)/x-3xy#?

##### 2 Answers

Long time since tried this but I am having a go!

#### Explanation:

Using std forms

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let

then

Let

then

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Collecting like terms

By working step-wise taking derivatives of individual components you should end up with

#### Explanation:

This is complex so check carefully before assuming what follows is valid:

Breaking the equation up into small pieces and working on the derivatives for each:

Part 1: The

Finding the derivative of

so

Part 2: The

Finding the derivative of

with

so

Part 3: The

Finding the derivative of

with

so

Part 4: The

from Part 1 we already have

Putting the pieces together

Take the derivative of both sides