I just want to make sure I am doing this correctly
d/dx(e^5x + 1) = 5e^5x
and
find d2/dx2 (lnx)^3 = 6(lnx)
The first one is correct.
However, the second one is missing something...
$\displaystyle \frac{d^2}{dx^2}(\ln(x))^3$
You need to apply the chain rule here...
$\displaystyle \frac{d}{dx}(\ln(x))^3=3(\ln(x))^2\cdot\frac{1}{x} =\frac{3(\ln(x))^2}{x}$
$\displaystyle \frac{d}{dx}\frac{3(\ln(x))^2}{x}=\frac{6\ln(x)-3(\ln(x))^2}{x^2}$
Hope this makes sense!
--Chris