Differentiate and simplify please help?
Using the chain rule,
Use the product rule,
The derivate of
The derivative of
We shall use logarithmic differentiation - that is, we will take the natural log of both sides and differentiate implicitly w.r.t
Take the natural log (
Applying the power rule of natural log
Differentiate both sides implicitly w.r.t
To differentiate the RHS, we will need to use the product rule!
By the product rule:
Substituting we get:
Going back to what we had before:
We want to isolate
We want to write everything in terms of