So, these two are equal to each other as well which tells me that this derivative, Cp dH/dT constant pressure is Cp.

所以这两者也相等,这告诉我们在恒压下微分，等于。

麻省理工公开课 - 热力学与动力学课程节选

Then we can take the derivative of that quantity, when we vary the temperature, holding the volume constant.

即恒定体积，改变温度，这里恒定温度下。

麻省理工公开课 - 热力学与动力学课程节选

If you're taking only one derivative you can add a constant.

如果只进行一次求导,你可以添加一个常数项

耶鲁公开课 - 基础物理课程节选

And the mathematics of that equation involved a double derivative in time of x 0 plus some constant times x equals zero with some constraints on it.

那个数学方程式,包括了x对时间的二阶导数,加上常数乘以x等于,还有一些限制条件。

麻省理工公开课 - 固态化学导论课程节选

Everyone knows from calculus that if you're trying to find a function about which you know only the derivative, you can always add a constant to one person's answer without changing anything.

学过微积分的人都知道,如果你想根据已知的导数,求出其原函数,你总是可以给某人的答案,随便加一个常数,且不影响结果

耶鲁公开课 - 基础物理课程节选

du/dT constant pressure is the direct derivative with respect to temperature here, which is sitting by itself under constant volume keeping this constant but there is temperature sitting right here too.

偏U偏T，p恒定是对,温度的直接微分，而它本身对体积不变,保持它不变，但是这里也有一个温度,这就是偏U偏V，T恒定。

麻省理工公开课 - 热力学与动力学课程节选

take the derivative of this, get the velocity vector and you notice his magnitude is a constant Whichever way you do it, you can then rewrite this as v square over r.

对这个式子求一次导,就能得到速度矢量,你会发现其模长是常数,不管用什么方法,加速度也可以写成 v^2 / r

耶鲁公开课 - 基础物理课程节选

OK, so for a constant volume process, du we can write du, partial derivative of dT u with respect to T at constant V, dT, dv plus partial derivative of u at constant V, dV.

好，对于一个恒定体积的过程，我们可以写出,等于偏u偏T，V不变，加上偏u偏V，T不变。

麻省理工公开课 - 热力学与动力学课程节选