Question

Find the derivative of f(x) = negative 7 divided by x at x = -3.

Answer 1

f(x)=-7/x

dy/dx=(-1*-7)/x^2

dy/dx=7/x^2

dy/dx(-3)=7/(-3)^2

dy/dx(-3)=7/9

Answer 2

The derivative of f(x) at x= -3 is:

`f'(-3)=(-7)/(9)`

Explanation:

The function f(x) is given by:

`f(x)=(-7)/(x)`

We are asked to find the derivative of x at x= -3

We know that the derivative of f(x) at x=a is calculated by using the formula:

`f'(a)= \lim_(h \to 0) (f(a+h)-f(a))/(h)`

i.e.

`f'(-3)= \lim_(h \to 0) ((7)/(-3+h)-(7)/(-3))/(h)\\\\i.e.\\\\f'(-3)=\lim_(h \to 0) ((7* (-3)-7* (h-3))/((-3)(-3+h)))/(h)\\\\f'(-3)=\lim_(h \to 0) (-21-7h+21)/(h(h-3)(-3))\\\\f'(-3)=\lim_(h \to 0) (-7h)/(h(h-3)(-3))\\\\f'(-3)=\lim_(h \to 0) (-7)/((h-3)(-3))\\\\f'(-3)=(-7)/(9)`