Question

differentiate the function

f(x)=xlnx-x

Answer 1

We need a couple of rules...
Difference rule.
Product rule.

Answer 2

\[[x \ln(x)-x]' \\ [x \ln(x)]'-[x]' \text{ by difference rule } \\ [x]' \ln(x)+x [\ln(x)]'-[x]' \text{ by product rule }\]

Answer 3

do you know the derivative of x w.r.t. x?
and also do you the derivative of ln(x) w.r.t. x?

Answer 4

would i use the log rule to find the derivative of lnx

Answer 5

can you show me what rule you mean?

Answer 6

\[\ln g(x)=g \prime/g\]

Answer 7

you can use that

Answer 8

except it should be [ln(g(x))]'=g'/g