Answer:
The derivative of given function is 2.
Step-by-step explanation:
The given function is
[tex]s(x)=2x+6[/tex]
We need to use
[tex]f'(x)=lim_{h\rightarrow 0}\dfrac{f(x+h)-f(x)}{h}[/tex]
to find the derivative of given function.
[tex]s'(x)=lim_{h\rightarrow 0}\dfrac{s(x+h)-s(x)}{h}[/tex]
[tex]s'(x)=lim_{h\rightarrow 0}\dfrac{2(x+h)+6-(2x+6)}{h}[/tex]
[tex]s'(x)=lim_{h\rightarrow 0}\dfrac{2x+2h+6-2x-6)}{h}[/tex]
[tex]s'(x)=lim_{h\rightarrow 0}\dfrac{2h}{h}[/tex]
[tex]s'(x)=lim_{h\rightarrow 0}2[/tex]
Apply limit.
[tex]s'(x)=2[/tex]
Therefore, the derivative of given function is 2.
