Math Help - The bloody derivitives!

1. The bloody derivitives!

What is the derivitive and method(of getting the derivitive) of
f'(x)=-10/(3x+2)^2

Thanks guys.

2. As it's written, you must find $f(x),$ perform integration.

3. Originally Posted by Muhammed Ali
What is the derivitive and method(of getting the derivitive) of
f'(x)=-10/(3x+2)^2

Thanks guys.
Initial equation
$f\prime (x)=-\frac{10}{(3x+2)^2}$

Take the derivative
$f\prime\prime(x)=\frac{d}{dx}\frac {-10}{(3x+2)^2}$

-10 is a coefficient, so we can write

$f\prime\prime(x)=-10\left[\frac{d}{dx}\frac 1{(3x+2)^2}\right]$

Then we rewrite without the fractions
$f\prime\prime(x)=-10\left[\frac{d}{dx}(3x+2)^{-2}\right]$

Use the product rule to move the negative 2 out front, and subtract 1 from the exponent making it negative 3, and the chain rule to take the derivative of the inside of the exponent.
$f\prime\prime(x)=-10(-2)(3x+2)^{-3}\left[\frac{d}{dx}(3x+2)\right]$

Use the power rule to turn d\dx(3x+2) into 3
$f\prime\prime(x)=-10(-2)(3x+2)^{-3}(3)$

Combine coefficients
$f\prime\prime(x)=60(3x+2)^{-3}$

Write as a fraction
$f\prime\prime(x)=\frac{60}{(3x+2)^3}$

4. Originally Posted by Muhammed Ali
What is the derivitive and method(of getting the derivitive) of
f'(x)=-10/(3x+2)^2

Thanks guys.
Are you saying you want to differentiate f'(x) to get f''(x).

Or did you mean to say you want to integrate f'(x) to get f(x).

5. Well, I got my first derivative wrong, so I'm dumb. But now I have everything figured out, thanks guys.