Answer:
[tex]\frac{d}{dx} f(x) =-10[/tex]
General Formulas and Concepts:
Calculus
- Derivative Notation
- Definition of a Derivative: [tex]\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
f(x) = -10x
Step 2: Find Derivative
- Substitute: [tex]\frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10(x + h)-(-10x)}{h}[/tex]
- Distribute -10: [tex]\frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10x -10h-(-10x)}{h}[/tex]
- Distribute -1: [tex]\frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10x -10h+10x}{h}[/tex]
- Combine like terms: [tex]\frac{d}{dx} f(x)= \lim_{h \to 0} \frac{-10h}{h}[/tex]
- Divide: [tex]\frac{d}{dx} f(x)= \lim_{h \to 0} -10[/tex]
- Evaluate: [tex]\frac{d}{dx} f(x)=-10[/tex]
