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

Hence, the value of derivative is:

-5

Explanation:

We are given a function f(x) by:

`f(x)=(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) (f(a+h)-f(a))/(h)`

Here a= -1

Hence, we have:

`f'(-1)= \lim_(h \to 0) (f(-1+h)-f(-1))/(h)\\\\\\f'(-1)= \lim_(h \to 0) ((5)/(-1+h)-(5)/(-1))/(h)\\\\\\i.e.\\\\\\f(-1)= \lim_(h \to 0) ((5* (-1)-5* (h-1))/((-1+h)(-1)))/(h)\\\\\\f(-1)=\lim_(h \to 0) (-5-5h+5)/(h(h-1)(-1))\\\\\\f(-1)=\lim_(h \to 0) (-5h)/((-1)(h-1)h)\\\\\\f(-1)=\lim_(h \to 0) (5)/((h-1))\\\\\\f(-1)=-5`

Hence, the answer is: -5