Question

Find the derivative of f(x) = 5 divided by x at x = -1.

Answer 1

5/x = 5/ -1= -5
f(x)=-5 i think

Answer 2

Answer:

Hence, the value of derivative is:

                         -5

Step-by-step explanation:

We are given a function f(x) by:

$f(x)=\dfrac{5}{x}$

We know that the derivative of a function at x=a is calculated by using the method

$f'(a)= \lim_{h \to \0} \dfrac{f(a+h)-f(a)}{h}$

Here a= -1

Hence, we have:

$f'(-1)= \lim_{h \to 0} \dfrac{f(-1+h)-f(-1)}{h}\\\\\\f'(-1)= \lim_{h \to 0} \dfrac{\dfrac{5}{-1+h}-\dfrac{5}{-1}}{h}\\\\\\i.e.\\\\\\f(-1)= \lim_{h \to 0} \dfrac{\dfrac{5\times (-1)-5\times (h-1)}{(-1+h)(-1)}}{h}\\\\\\f(-1)=\lim_{h \to 0} \dfrac{-5-5h+5}{h(h-1)(-1)}\\\\\\f(-1)=\lim_{h \to 0} \dfrac{-5h}{(-1)(h-1)h}\\\\\\f(-1)=\lim_{h \to 0} \dfrac{5}{(h-1)}\\\\\\f(-1)=-5$

    Hence, the answer is: -5