the function y=e^x is its own derivitive. Show that for very value of c, y=c(e^x) has the same property

You could use the product rule:  

assuming that f(x) = a(x)·b(x)

then               f'(x) = a(x)·b'(x) + b(x)·a'(x)

 

For the problem  f(x)  =  x·e^x, let a(x) = c  and  b(x) = e^x,   (which makes a'(x) = 0 and b'(x) = e^x)

then                   f'(x) = c·e^x + e^x·0

so                      f'(x) = c·e^x