# what is the derivative function log(f(x+y)) with respect to x?

I have the function of alpha + beta log(gamma((alpha+beta))), I want to calculate the derivative this function with respect to alpha. I need it as a derivative of inverted beta-liouville function with respect to each of its parameters.enter image description here

• Can you work with a numerical approximation or do you need the actual analytical solution? If the numerical approximation is OK, doing a (cubic) spline interpolation for example can be much simpler to derive.
– PC1
Jun 14 at 15:39
• Welcome to MSE! Please learn to use MathJax so you can write formulas: math.meta.stackexchange.com/questions/5020/… Jun 14 at 15:50
• The derivative of digamma is the trigamma function. Use the sum rule and chain rule to complete the solution. Jun 14 at 15:59
• You can use JAX to compute the derivatives: jax.readthedocs.io/en/latest/_autosummary/… Jun 14 at 16:59
• @PC1 I actually need its general formula not as a values, cause I want to calculate the maximum likelihood with respect to each parameter Jun 14 at 18:42