Question

\(\dfrac{d}{dx}\left(\dfrac{1}{3x-2}\right)=\) ?

• A. \(-\dfrac{1}{(3x-2)^2}\)
• B. \(-\dfrac{3}{(3x-2)^2}\)
• C. \(\dfrac{3}{(3x-2)^2}\)
• D. \(\dfrac{3}{3x-2}\)

Hint:

General form: \(\dfrac{d}{dx}(ax+b)^{-1}=-a(ax+b)^{-2}\).

Answer 1

The Correct Option is B

Idea. Write as a negative power and apply the chain rule.
\[ (3x-2)^{-1}\ \Rightarrow\ \frac{d}{dx}(3x-2)^{-1}=-1(3x-2)^{-2}\cdot(3) =-\frac{3}{(3x-2)^2}. \]