Question

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

Answer 1

`(d)/(dx) f(x) =-10`

General Formulas and Concepts:

Calculus

• Derivative Notation
• Definition of a Derivative:
  `\lim_(h \to 0) (f(x+h)-f(x))/(h)`

Explanation:

Step 1: Define

f(x) = -10x

Step 2: Find Derivative

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