Use the 4 step process to find the f' (x) of the function f (x) = x^2-3/2

see below

Step-by-step explanation:

Modified problem

(x) ^2-3/x

Step 1: Find f (x+h)

(x+h) ^2-3 / (x+h)

x^2 + 2hx + h^2 - 3 / (x+h)

Step 2: Find f (x + h) - f (x)

x^2 + 2hx + h^2 - 3 / (x+h) - (x^2-3/x)

Distribute the minus sign

x^2 + 2hx + h^2 - 3 / (x+h) - x^2+3/x

Combine like terms and get a common denominator

2hx + h^2 - 3x / (x (x+h)) + 3 (x+h) / (x (x+h)

2hx + h^2 + 3h / (x (x+h))

Step 3: Find (f (x + h) - f (x)) / h

(2hx + h^2+3h / (x (x+h))) / h

2hx/h + h^2/h+3h / (x (x+h)) / h

2x + h + 3 / (x (x+h))

Step 4: Find lim h→0 (f (x + h) - f (x)) / h

2x+0 + 3 / (x (x+0))

2x + 3/x^2