Estimate $\ln\left( 1.04^{0.25} + 0.98^{0.2} -1 \right)$ with 2D Taylor I need to estimate $\ln\left( 1.04^{0.25} + 0.98^{0.2} -1 \right)$ with a Taylor approximation of a two variable function (i.e. x and y).
Eventually I managed to pull the (presumably) correct function:
$$f(x,y) = \ln \left( (1+2x)^{\frac{5}{4}y} - (1-x)^y - 1 \right)$$
around $\left( 0, 0.2 \right)$.
But its partial derivatives are overly complicated, see examples for $f_{xx}$ and $f_{yx}$.
So my best guess for the function is wrong. It feels like I'm missing an identity that would simplify the task.  
Could you please direct my towards the most appropriate function?

My opinion is that you complicate things too much. Just try $f(x,y)=\ln (x^{0.25} + y^{0.02} -1)$ around $(1,1)$.
