Question

can you please find the derivative of this
$x ln(x)$
answer must be
$ln(x) + 1$
​

Answer 1

Step-by-step explanation:

d( f(X)•g(X))/dx=d(f(X))/dx •g(X) +d(g(X))/dx•f(X)

basically derivative of 2 functions multiplied to each other is the dervitive of the function times the second function plus the derivitive of the second function times the first. think of differentiating one and assuming the other is some constant at each step. this is called the product rule or UV rule(search online)

using that here

d(ln(X))/dx•x + d(X)/dx•ln(X)

= (1/X)•X + (1)• ln(X)

=1 + ln(X)