Question

d/dx (x log x) is equal to

(a) log e(ex) (b) 1/log x

(c) log x (d) x/log x​

Answer 1

Step-by-step explanation:

By applying product rule,

$\dfrac{d}{dx} ( f(x) · g(x)) = f(x)'·g(x)+f(x)·g(x)'$

$\dfrac{d}{dx} (x log(x)) = \dfrac{d}{dx}(x)·log(x) +x·\dfrac{d}{dx}(log(x))$

$= log(x) +x·\dfrac{1}{x}=log(x)+1$