More Calculus, YEAH!!!!!!!!!?

Question

Find the dirivative of the following function using the limit definition:

f(x)= 3-x^2/ 2 +x

Answer 1

f(x)= 3-x^2/ 2 +x
f'(x)=[-2x(2+x)-(3-x^2)]/(2+x)^2
f'(x)=[-(x+3)(x+1)]/(2+x)^2

Answer 2

The way you've typed it you mean a (or do you mean one of the others??)

a) f(x)= 3 - [x^2/ 2] + x

b) f(x)= [3-x^2]/ [2 + x]

c) f(x)= [3-x^2]/ 2] + x

d) f(x)= 3 - [x^2]/ [ 2 + x]

The limit definition of derivative (one def) is

Lim as h-->0 [f(x-h) - f(x)] / h

(but I'm not abt to use the definition unless I know the function.)