This is a group which, I feel, it is acceptable to assume that they have at least an interest in maths if not a fair understanding. Here is the 'joke':
Note that it begins by defining a function: f(a). This means that f is a function of a only. Now it goes on to state that f is given by the nth root (and in a stupid way, personally I would have gone with the power of 1/n) of Euler's number raised to the power of x. Now since f is a function of 'a' only, n and x must be constant. Since 'a' does not appear in the definition, f is, therefore, a constant. At this stage I have ignored the fact that the 'function' is quite loosely 'defined'.
Next we decide to take the limit of f(a) - (1/f(t)) as t approaches infinity for no apparent reason. We also set it equal to the derivative with respect to x of f(u), again, for no apparent reason.
In the next line the limit expression remains EVEN THOUGH WE HAVE APPLIED THE LIMIT. Also, the infinity symbol appears in the expression. This symbol is not supposed to be used in this manner. If you had a limit which was one divided by something which went to infinity in that limit, you would express the limit as zero - NOT 1 divided by infinite. Beyond that, f is defined to be a constant. The limit as t goes to infinity of f is that same constant. Therefore the constant must be infinity!
However note that on the right hand side of the equation we are taking the derivative with respect to x of a function of u, which must therefore be zero. This means that f(a), which is a constant, must be zero. BUT WE JUST MADE THE CLAIM IT MUST BE INFINITY!
Next we substitute the expression for f(a) into the expression and ignore the fact that the derivative on the right hand side is zero. Now we raise both sides to the power of n. Now I find the right hand side of equation to be quite interesting. Because they have made so many errors so far and obviously don't actually realise that the derivative is zero, and hence assume that f(u) somehow has some sort of x dependency. If f(u) was dependent on x, the entire expression would need to be to the power of n, derivative and all.
Given that, when both sides were integrated (indefinitely), the fundamental theorem of calculus would not apply as it is no longer the integral of a derivative. Also, I have never heard of the fundamental theorem of calculus being applied to an indefinite integral, only definite ones.
In conclusion this entire 'joke' is equivalent to just writing "sex is fun!" and then it being circulated on the internet with everyone commenting on how funny it is.