Y = log the derivative of the logarithm of x ^ 2 + X + 1 with a as the base This is an exercise at the back of the book.

Y = log the derivative of the logarithm of x ^ 2 + X + 1 with a as the base This is an exercise at the back of the book.

y'=[1/(x^2+x+1)lna]*(x^2+x+1)'
=(2x+1)/(x^2+x+1)lna

Why LNY becomes y '/ Y on the left side of logarithmic derivation

First, we derive LN
It's 1 / y
Then y is a function of X
So we have to take the derivative of Y, which is y

To find the derivative of the root sign T / (T + 1), the logarithmic differential method is used,
The answer is: 1 / (2 radical T) (T + 1) ^ 3 / 2

Take logarithm on both sides
ln(y) = ln(t) / 2 - ln(t+1) /2
The derivation of T on both sides is determined by the chain rule
{ln(y)]' = 1/y * y' = 1/(2t) - 1/(2t+2) = 1 / [2(t+1)t]
So y '= Y / [2 (T + 1) t] = 1 / (2 * T ^ (1 / 2)) (T + 1) ^ 3 / 2