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