Use the definition of the derivative to find the derivative of the function .
Answer

Question

Use the definition of the derivative to find the derivative of the function $$ f(x)=22 $$. Answer

UpStudy AI · Accepted Answer

1. The derivative of a function is defined as  
   $$
   f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}.
   $$

2. For the function $$ f(x)=22 $$, we have  
   $$
   f(x+h)=22.
   $$

3. Substituting into the definition, we get  
   $$
   f'(x)=\lim_{h \to 0}\frac{22-22}{h}=\lim_{h \to 0}\frac{0}{h}.
   $$

4. Since $$\frac{0}{h}=0$$ for all $$h \neq 0$$, the limit becomes  
   $$
   f'(x)=\lim_{h \to 0}0=0.
   $$

Therefore, the derivative of the function is  
$$
f'(x)=0.
$$
The derivative of $$ f(x)=22 $$ is 0.

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