Is $\exp(x)$ the same as $e^x$? For homework I have to find the derivative of $\text {exp}(6x^5+4x^3)$ but I am not sure if this is equivalent to $e^{6x^5+4x^3}$ If there is a difference, what do I do to calculate the derivative of it? 

As other answers say, in your homework (and, indeed, in most places in mathematics) there is no difference.  
I have seen a beginning textbook first defining a certain function $\exp(x)$, then proving certain properties of it, and finally using those properties to motivate calling it $e^x$.
