# Question:Three Questions: Function defined by derivative, function define d by Integral,

## Question:Three Questions: Function defined by derivative, function define d by Integral,

Maple 2023

First Question

Let's define a function:

 (1.1)

now define a new function that is the derivative of f.

 (1.2)

g is not what I expected. I expect:

and if i try to calculate g(0), the result is:

 (1.3)

Second Question

I need to define an integral function in which the variable is an integration boundary:

 (2.1)

if I try to calculate :

 (2.2)

how can i do the calculation and display the explicit form of the function, and assign to a name ?

 (2.3)
 Third Question is there a way to write a system of equation in text mode (or math) in the usual math notation with a big curly bracket followed by the list of equation ? graphically similar to the piecewice operator that seems to be not useful for this purpose?

About the first and the second question i read on the web something but i don't understand deeply what is the reason of the behaviour. I would like to understand really that. Thanks a lot.