Question

what is the derivative quotient of 6x-5/2x-1

Answer 1

What is the derivative quotient of $\frac{6x - 5}{2x - 1}$?

Solution:

The rule states that the derivative of $\frac{f(x)}{g(x)}$ is

$$\left(\frac {\mathrm {f (x)}}{\mathrm {g (x)}}\right) ^ {\prime} = \frac {\mathrm {f ^ {\prime} (x) g (x) - g ^ {\prime} (x) f (x)}}{g ^ {2} (x)}$$

For $\frac{6x - 5}{2x - 1}$ it will be

$$\begin{array}{l} \left(\frac {6 x - 5}{2 x - 1}\right) ^ {\prime} = \frac {(6 x - 5) ^ {\prime} (2 x - 1) - (2 x - 1) ^ {\prime} (6 x - 5)}{(2 x - 1) ^ {2}} = \frac {6 (2 x - 1) - 2 (6 x - 1)}{(2 x - 1) ^ {2}} \\ = \frac {1 2 x - 6 - 1 2 x + 2}{(2 x - 1) ^ {2}} = \frac {- 4}{(2 x - 1) ^ {2}} \\ \end{array}$$

Answer: $\frac{-4}{(2x - 1)^2}$