f(x) = 3/x(lnx)^2
f(x)' = ?
This one is tricky, can someone explain?

Question

f(x) = 3/x(lnx)^2
f(x)' = ?
This one is tricky, can someone explain?

ddcamp · Answer

Start by rewriting this in a form that's more friendly for the power rule:
$$\frac{ 3 }{ x \ln (x)^2 } \rightarrow 3x^{-1}\ln(x)^{-2}$$

ddcamp · Answer

Then, use the power rule:
Identify f(x) and g(x):
$$f(x) = 3x^{-1} \ g(x) = \ln(x)^{-2}$$
and now find f'(x) and g'(x):
$$f'(x) = -3x^{-2} \ g'(x) = (-2\ln(x)^{-3})x^{-1}$$
G'(x) found using the chain rule

anonymous · Answer

$$\int\limits \left(-\frac{3 (\log (x)+2)}{x^2 \log ^3(x)}\right) \, dx=\frac{3}{x \text{Log}[x]^2} $$