Question

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

Answer 1

Answer:

$\frac{3}{16}$

Step-by-step explanation:

Hello, I think  I can help you with this

let's remember

$\frac{1}{x^{n} } =x^{-n} \\and\\\frac{dy}{dx} x^{n}=nx^{n-1}$

Let

$f(x)=-\frac{3}{x} \\f(x)=y\\y=-\frac{3}{x}$

Step 1

derive

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

$y=-\frac{3}{x}\\y=-3*x^{-1}\\ y'=-3(-1x^{-1-1})\\ y'=-3(-1x^{-2})\\y'=3x^{-2}\\ y'=\frac{3}{x^{2}}$

Step 2

fin y'(-4)

Put the value of -4 in the equation

$y'=\frac{3}{x^{2}}\\ y'(-4)=\frac{3}{(-4)^{2}}\\y'(-4)=\frac{3}{16}$

Have a great day

Answer 2

Hope this helps you.