Question

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

Answer 1

Use the product rule. `y'=ln(x)+1`.

Explanation:

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)`

In the case of `y=xln(x)`, `f(x)=x` and `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`.

Putting it all together, we get `y'=ln(x)+1`.

Hope this helps!