I've been working through my practice problems and came across one that has stumped me.
What I'm not understanding is where the (6x ln x)/(3x^2+2) comes from, if anyone could explain this.
The answer to this is:
What I'm coming up with is:
What I'm not understanding is where the comes from, if anyone could explain this I'd really appreciate it.
Answer & Explanation
Using logarithmic differentiation, that is,
Now, when you take the derivative, the left-hand side becomes
Use the product rule on the right-hand side, and don't forget Thus, altogether you'll get
Above, the 6x comes from the chain rule. Multiply both sides by and we get
We can perhaps go a little further in simplification to get
Here, I have factored a from each term, thus the second term will get a square in the denominator, and the factor in front of the fraction gets an extra +1 in the numerator.