SciLearn: differential table

This is a table that lists everything in differentials, so it can be used for differentiation and integration at the same time.

I'm not sure if everyone can find this useful, since some might prefer non-differential forms because they are easier to understand and use - so I don't think this table would be suitable for calculus beginners.

Okay, here's what the symbols in my table means:

k is a constant;
f, g are functions of a variable t.

And here's the table (click the image if the equations get cropped):
$\begin{array}{ll}d \left( f \cdot g \right) = df \cdot g + f \cdot dg &d \left( \frac{f}{g} \right) = \frac{df \cdot g - f \cdot d g}{g^2} \\d \left( f^k \right) = k f^{k - 1} df &d \left( f^g \right) = g f^{g - 1} \, df + f^g \ln f dg \\d \left( k^f \right) = k^f \ln k \, df &d \log_k f = d \left( \frac{\ln f}{\ln k} \right) = \frac{df}{f \ln k} \\d \left( e^t \right) = e^t dt &d \ln t = \frac{dt}{t} \\d \sin t = \cos f \, dt &d \cos t = - \sin t \, dt \\d \tan t = \sec^2 t \, dt &d \cot t = - \csc^2 t \, dt \\d \sec t = \sec t \tan t \, dt &d \csc t = - \csc t \cot t \, dt \\d \arcsin t = - d \arccos t = \frac{d t}{\sqrt{1 - t^2}} \\d \arctan t = - d \operatorname{arccot} t = \frac{d t}{1 + t^2} \\d \operatorname{arcsec} f = - d \operatorname{arccsc} t = \frac{dt}{|t| \sqrt{-1 + t^2}} \\d \sinh t = \cosh t \, dt &d \cosh t = \sinh t \, dt \\d \tanh t = \operatorname{sech}^2 t \, dt &d \coth t = - \operatorname{csch}^2 t \, dt \\d \operatorname{sech} t = - \operatorname{sech} t \tanh t \, dt &d \operatorname{csch} t = - \operatorname{csch} \coth t \, dt \\d \operatorname{arsinh} t = \frac{dt}{\sqrt{1 + t^2}} &d \operatorname{arcosh} t = \frac{dt}{\sqrt{-1 + t^2}} \\d \operatorname{artanh} t = d \operatorname{arcoth} t = \frac{dt}{1 - t^2} \\d \operatorname{arsech} t = - \frac{dt}{t \sqrt{1 - t^2}} &d \operatorname{arcsch} t = - \frac{dt}{|t| \sqrt{1 + t^2}}\end{array}$

You can tell me if this is useful or not.