# How do you find the derivative of s=-3/(4t^2-2t+1)?

May 25, 2017

$\frac{24 t - 6}{4 {t}^{2} - 2 t + 1} ^ 2$ Through the quotient rule (see below).

#### Explanation:

The quotient rule states:

$\frac{\left(L o w \cdot \mathrm{dH} i g h\right) - \left(H i g h \cdot \mathrm{dL} o w\right)}{L o w} ^ 2$

So we need to determine the derivative of the top or the "dHigh" and the derivative of the bottom or the "dLow."

The derivative of the top, or "dHigh" is the derivative of -3, which is 0.

The derivative of the bottom, or "dLow" is the derivative of 4t^2−2t+1

From the Power Rule of Derivatives, we know the derivative of that is:
$8 t - 2$

From this we can plug everything back into the above equation from the quotient rule. So we get the following after simplification:

$\frac{24 t - 6}{4 {t}^{2} - 2 t + 1} ^ 2$