Question

Find the derivative using the limit process of f (x) = - 10x

Answer 1

Answer:

$\frac{d}{dx} f(x) =-10$

General Formulas and Concepts:

Calculus

• Derivative Notation
• Definition of a Derivative: $\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Step-by-step explanation:

Step 1: Define

f(x) = -10x

Step 2: Find Derivative

1. Substitute:                         $\frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10(x + h)-(-10x)}{h}$
2. Distribute -10:                    $\frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10x -10h-(-10x)}{h}$
3. Distribute -1:                      $\frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10x -10h+10x}{h}$
4. Combine like terms:         $\frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10h}{h}$
5. Divide:                               $\frac{d}{dx} f(x)= \lim_{h \to 0} -10$
6. Evaluate:                           $\frac{d}{dx} f(x)=-10$