Question

The derivative of the quotient of two functions is the quotient of derivatives of those two functions.

• A. True
• B. False

Answer 1

The correct option is B False

At first it sounds to be a correct statement, Right? But it’s not. We have discussed in the videos that if let’s say f(x) and g(x) are the two functions then the derivative of their quotient i.e.,
$\frac{d}{dx}\left(\frac{f\left(x\right)}{g\left(x\right)}\right)=\frac{g\left(x\right)\left(f^{\prime }\right(x\left)\right)-f\left(x\right)\left(g^{\prime }\right(x\left)\right)}{\left(g\right(x){)}^2}$
Please remember that in the numerator of the derivative, the numerator of the function is differentiated first and then in the second term the denominator is differentiated.
So the statement is false.