Hence, the value of derivative is:
-5
We are given a function f(x) by:
[tex]f(x)=\dfrac{5}{x}[/tex]
We know that the derivative of a function at x=a is calculated by using the method
[tex]f'(a)= \lim_{h \to \0} \dfrac{f(a+h)-f(a)}{h}[/tex]
Here a= -1
Hence, we have:
[tex]f'(-1)= \lim_{h \to 0} \dfrac{f(-1+h)-f(-1)}{h}\\\\\\f'(-1)= \lim_{h \to 0} \dfrac{\dfrac{5}{-1+h}-\dfrac{5}{-1}}{h}\\\\\\i.e.\\\\\\f(-1)= \lim_{h \to 0} \dfrac{\dfrac{5\times (-1)-5\times (h-1)}{(-1+h)(-1)}}{h}\\\\\\f(-1)=\lim_{h \to 0} \dfrac{-5-5h+5}{h(h-1)(-1)}\\\\\\f(-1)=\lim_{h \to 0} \dfrac{-5h}{(-1)(h-1)h}\\\\\\f(-1)=\lim_{h \to 0} \dfrac{5}{(h-1)}\\\\\\f(-1)=-5[/tex]
Hence, the answer is: -5
