# How do you find the derivative of y=xlnx?

#### Risposta:

Usa il regola del prodotto. y'=ln(x)+1.

#### Spiegazione:

You'll need the product rule for this one. The product rule is given by:

=(f(x)*g(x))'=f'(x)g(x)+f(x)g'(x)

Nel caso di y=xln(x), f(x)=x e g(x)=ln(x).

First we take the derivative of f(x). The derivative of a single variable (no coefficient, not raised to any power) is 1. We leave g(x) alone, so the first half of the derivative is simply 1*ln(x)=ln(x).

Then we take the derivative of g(x). The derivative of ln(x) is 1/x. We leave f(x) alone, so the second have of the derivative is x*1/x=1.

Mettendo tutto insieme, otteniamo y'=ln(x)+1.

Spero che questo ti aiuti!