Home » Blog » Compute derivatives of F(t) = log (1+t2) i + arctan t j + 1/(1+t2) k Compute derivatives of F(t) = log (1+t2) i + arctan t j + 1/(1+t2) k by RoRi May 31, 2016 Compute the derivatives and of the vector valued function We compute Related
and 
of the vector valued function ![\[ F(t) = \log(1+t^2) \mathbf{i} + \arctan t \mathbf{j} + \frac{1}{1+t^2} \mathbf{k}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-e5758bae5c81d279b7aa715e093cd031_l3.png "Rendered by QuickLaTeX.com")
![\begin{align*} F'(t) &= \left( \frac{2t}{1+t^2}, \frac{1}{1+t^2}, \frac{-2t}{(1+t^2)^2} \right) \\[9pt] F''(t) &= \left( \frac{2(1-t^2)}{(1+t^2)^2}, \frac{-2t}{(1+t^2)^2}, \frac{6t^2 - 2}{(1+t^2)^2} \right). \end{align*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-fb27ddffda9cebc93a812109438f048e_l3.png "Rendered by QuickLaTeX.com")
and of the vector valued function
I got F’ like here and F” as in the book.