# Derivatives – Do we solve the following maximization problem analytically?

Is it possible to solve the lambda value that maximizes the following equation analytically?

$$frac {1-e ^ {- 30 lambda}} {30 lambda} – e ^ {- 30 lambda}$$,

Then the derivative is equal to:

$$frac {e ^ {- 30 lambda}} { lambda} – frac {30} {900 lambda ^ 2} + frac {30e ^ {- 30 lambda}} {900 lambda ^ 2 } + 30e ^ {- 30 lambda} = 0$$,

Is it possible to obtain an analytical solution for lambda or should it be solved numerically?