Question

State whether this statement is true or false.
$\frac{d}{dx}\left(\frac{1}{f\left(x\right)}\right)=\frac{-f^{\prime }\left(x\right)}{{\left[f\right(x\left)\right]}^2}$

• A. True
• B. False

Answer 1

The correct option is A True

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

$=\frac{-1f^{{}^{\prime }}\left(x\right)}{{\left[f\left(x\right)\right]}^2}$

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