Differentiate and simplify please help?
2 Answers
Explanation:
Express
Using the chain rule,
Express
Use the product rule,
, where
The derivate of
The derivative of
Explanation:
We shall use logarithmic differentiation - that is, we will take the natural log of both sides and differentiate implicitly w.r.t
Given:
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!
We have
Let
Thus,
By the product rule:
Substituting we get:
Simplifying...
Going back to what we had before:
We want to isolate
We want to write everything in terms of