I've been stuck on this calc problem for a while:

Let $f$ be the function given by $f(x) =\ln(x+1)$ and let $g$ be the function given by $g(x) = x^{-1/2}$. At what value of $x$ do the graphs of $f$ and $g$ have perpendicular tangent lines?

$a. 0.484\\
b. 1.000\\
c. 1.358\\
d. 2.065$

Thank you!