Linearize a specific equation

Question

Is it possible to linearize this equation? I tried without success.

$$Y = \dfrac{a \cdot L1 \cdot \left(L1 \over L2\right)^X-L2}{a \cdot \left(L1 \over L2\right)^X-1}$$ I want something in

$Y' = AX' +B$

Answer 1

To linearize $f(x)$ at a particular $x_0$, use $f(x_0+h) \approx f(x_0) +hf'(x_0) $. This is just the first two terms of the Taylor series.

In your case, compute $Y'(X)$ (quotient rule, derivative of $a^x$) and use the above formule.