I got a problem that is causing me a headache. So differentiating $\frac {1}{12π}*c^2*h$.
According to the constant rule we can pull out the constant $\frac {1}{12π}$ and differenciate $c^2*h$ as two different variables using the chain rule along with the product rule? The problem here is that my solutions doesn't match the online calculators which are taking $c^2$ as a constant and therefore produce the following answer $c \cdot \frac {h}{6π}$. I don't understant what I'm I doing wrong
In the most general case, both $c$ and $h$ are functions of $t$. Then you can write:
$\frac{dV(t)}{dt}$
= $ \frac{1}{12 \pi}\frac{d}{dt}c^2(t)h(t)$
= $\frac{1}{12 \pi} \left( 2c(t)c'(t)h(t) + c^2(t)h'(t)\right)$.
That's as far as one can get until you tell us how $c$ and $h$ vary as functions of $t$.