Mathematics: Find the derivative of f(x) = negative 9 divided by x at x = -4

i dont know dudeStep-by-step explanation:...

Find the derivative of f(x) = negative 9 divided

rleiphart1

11.03.2022

The derivative of f'(x) = -9/x when x = 4 is 9/16.

Step-by-step explanation:

We are to find the derivative of $f(x) = \frac{-9}{x}$ and x= -4

$f(x) = \frac{-9}{x} = -9x^{-1}$

f'(x) = [f(x)]'

$f'(x) = (-9x)^{-1}$

We know that,

$(x^n)' = nx^{n-1} where n is a constant$

So, $f'(x) = -9(-1)x^{-1-1}$

$f'(x) = 9x^{-2} = \frac{9}{x^2}$

Therefore when x=-4 ,

$f'(-4)= \frac{9}{-4^2}$ $= \frac{9}{16}$

Therefore, the derivative of $f'(x)= \frac{-9}{x}$ when x= -4 is 9/16.

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