Question

differentiate the function f(x)= xln(x)-x

Answer 1

Use the Product rule: (uv)' = u'v+uv'

Answer 2

Of course the derivative of the "-x" part is just -1, so you have to use the Product Rule for xlnx

Answer 3

Where the derivative of ln(x)=1/x

Answer 4

Yeah, \(\large ln(x)=\dfrac{1}{x}\).

Answer 5

So we get: \(f'(x)=1 \cdot \ln x+x \cdot \dfrac{1}{x}-1\).

What does this simplify to?