# Math Help - differentiate

1. ## differentiate

how do u differentiate nlnnln(lnn)? i have the answer but I dont know how to do it. Please help explain how to differntiate 3 or more products.

2. Originally Posted by twilightstr
how do u differentiate nlnnln(lnn)? i have the answer but I dont know how to do it. Please help explain how to differntiate 3 or more products.
Do you mean:

$n\cdot \ln(n) \cdot \ln(\ln(n))~,~n \in \mathbb R^+$ ?

If so split the product into two factors:

$\left(n\cdot \ln(n) \right) \cdot \left( \ln(\ln(n)) \right)~,~n \in \mathbb R^+$

Now use the product rule. To differentiate the factors use product rule (1rst factor) or chain rule(2nd factor) respectively.

I've got

$\ln(\ln(n)) \cdot (\ln(n) + 1) + 1$

3. my work:
[1(lnn) + 1/n (n)][ln(ln(n))] + (1/lnn(1/n))nlnn

= (lnn + 1)[ln(lnn)] + 1

i think this is right. Thanks