Question

Find the derivative of f(x) = negative 3 divided by x at x = -4.

Answer 1

Hope this helps you.

Answer 2

`(3)/(16)`

Explanation:

Hello, I think I can help you with this

let's remember

`(1)/(x^(n) ) =x^(-n) \\and\\(dy)/(dx) x^(n)=nx^(n-1)`

Let

`f(x)=-(3)/(x) \\f(x)=y\\y=-(3)/(x) \\`

Step 1

derive

derivative of f(x)=derivative of y=y'

`y=-(3)/(x)\\y=-3*x^(-1)\\ y'=-3(-1x^(-1-1))\\ y'=-3(-1x^(-2))\\y'=3x^(-2)\\ y'=(3)/(x^(2))`

Step 2

fin y'(-4)

Put the value of -4 in the equation

`y'=(3)/(x^(2))\\ y'(-4)=(3)/((-4)^(2))\\y'(-4)=(3)/(16)`

Have a great day