That means it involves the first partial derivatives of whatever you put into it.

这意味着，不管放什么进去，都会包括一阶偏导。

And we have learned how to package partial derivatives into a vector, the gradient vector.

我们也知道了，如何将各个偏导组合成一个梯度向量。

You can get this either by implicit differentiation and the product rule, or you could get this just by putting here, here,and here the partial derivatives of this with respect to x, y, and z.

可以通过隐函数微分法和乘法法则得到，或者直接,把关于x，y，z的偏微分放进来。

So, we have to figure out what we mean by partial derivatives again.

因此，我们应该重新理解偏导数的含义。

So, critical points, remember, are the points where all the partial derivatives are zero.

临界点是，偏导数都为零的点。

And, we「ll actually learn how to compute their partial derivatives without having to do this because we」ll just have the usual methods for computing derivatives.

计算偏导数的办法没这么麻烦，因为我们有常规的方法，因此我们不需要通过定义去求偏导数。

On the basis of the advanced first order and second moment method, the partial derivatives of the failure probability to the distribution parameters of the process variables were formulated.

由求解失效概率的改进一次二阶矩法出发，给出了失效概率对中间变量分布参数偏导数的计算公式；

A partial differential equation is an equation that involves the partial derivatives of a function.

偏微分方程就是，跟函数各个偏导数有关的方程。

So the unknown is a function, and the equation will relate the partial derivatives of that function to each other.

未知量是一个函数，这个方程，将把函数的偏导数联系起来。

You don't need to bring a ruler to estimate partial derivatives the way that this problem asks you to.

你们不需要像这道题一样，用尺子去表示出偏导来。

In this paper, the extrapolation formulas of rocket engine performance parameters are established utilizing one isentropic reference line and two partial derivatives for fixed enthalpy.

本文利用一条等熵参考线和两个等焓偏导数建立了火箭发动机性能参数的外推公式。

It has only partial derivatives for each variable.

它只有关于每个变量的偏导数。

Suppose and have continuous partial derivatives on.

设，在上有连续的偏导数。

Now you see how the total differential accounts for, somehow, all the partial derivatives that come as coefficients of the individual variables in these expressions.

现在可以看到，全微分里面的这些偏导数系数，都可以用一个变量表示出来。

Evaluation relevant to the partial derivatives of the multivariable functions is often done in scientific computation, usually by means of the symbolic differentiation or the divided difference.

科学计算及其应用常常需要多变量函数的有关偏导数问题的计算，通常使用的计算方法是符号微分或差分近似。