Answer:
f'(x) = 1
General Formulas and Concepts:
Calculus
- Limit Properties: [tex]\lim_{n \to a} c = c[/tex]
- Definition of a Derivative: [tex]f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
f(x) = x + 2
Step 2: Find derivative
- Substitute: [tex]f'(x)= \lim_{h \to 0} \frac{((x + h) + 2)-(x+2)}{h}[/tex]
- Distribute: [tex]f'(x)= \lim_{h \to 0} \frac{x + h + 2-x-2}{h}[/tex]
- Combine like terms: [tex]f'(x)= \lim_{h \to 0} \frac{h}{h}[/tex]
- Divide: [tex]f'(x)= \lim_{h \to 0} 1[/tex]
- Evaluate: [tex]f'(x)= 1[/tex]
