differential coefficient

简明释义

差动系数

英英释义

例句

1.To find the differential coefficient 微分系数, we need to take the derivative of the function with respect to its variable.

要找到微分系数 微分系数，我们需要对函数相对于其变量进行求导。

2.The differential coefficient 微分系数 can be interpreted as the instantaneous rate of change of a quantity.

微分系数 微分系数可以被解释为某一量的瞬时变化率。

3.In physics, the differential coefficient 微分系数 of position with respect to time gives us the velocity.

在物理学中，位置对时间的微分系数 微分系数给出了速度。

4.When calculating the differential coefficient 微分系数, it's important to consider the limits involved.

在计算微分系数 微分系数时，考虑相关的极限是很重要的。

5.In calculus, the differential coefficient 微分系数 of a function at a point gives the slope of the tangent line at that point.

在微积分中，函数在某一点的微分系数 微分系数表示该点切线的斜率。

作文

In the realm of calculus, the concept of the differential coefficient plays a crucial role in understanding how functions behave. The differential coefficient, often referred to as the derivative, measures the rate at which a function changes at any given point. To put it simply, it tells us how steep a curve is at a specific point and provides valuable insights into the function's behavior. To grasp the significance of the differential coefficient, let's consider a practical example involving motion. Imagine a car traveling along a straight road. The position of the car can be described by a function that relates time to distance. If we want to know how fast the car is moving at a particular moment, we need to find the differential coefficient of the position function. This allows us to determine the instantaneous velocity of the car, which is essential for understanding its motion. Mathematically, the differential coefficient is defined as the limit of the average rate of change of the function as the interval approaches zero. This is expressed as:f'(x) = lim (h -> 0) [f(x + h) - f(x)] / hIn this formula, f'(x) represents the differential coefficient of the function f at the point x. The variable h signifies a small change in x, and as h approaches zero, we obtain the precise rate of change at that specific point.The differential coefficient is not just a theoretical concept; it has numerous practical applications. For instance, in physics, it helps in calculating acceleration, which is the differential coefficient of velocity with respect to time. In economics, it can be used to analyze how changes in price affect the demand for a product. In biology, the differential coefficient aids in modeling population growth rates, allowing scientists to predict future population sizes based on current data.Furthermore, the differential coefficient also has geometric interpretations. It represents the slope of the tangent line to the curve of the function at a given point. By understanding this slope, we can visualize how the function behaves locally. If the differential coefficient is positive, the function is increasing at that point; if it's negative, the function is decreasing. If the differential coefficient equals zero, it indicates a potential maximum or minimum point, where the function may change direction.In conclusion, the differential coefficient is an essential concept in calculus that provides insights into the behavior of functions. Whether in physics, economics, or biology, its applications are vast and varied. By comprehending the differential coefficient, we gain a powerful tool for analyzing change and understanding the world around us. As we continue to explore the intricacies of calculus, the importance of the differential coefficient will undoubtedly remain a cornerstone of mathematical analysis.

在微积分的领域中，differential coefficient（微分系数）的概念在理解函数行为方面起着至关重要的作用。differential coefficient通常被称为导数，它测量函数在任何给定点的变化速率。简单来说，它告诉我们曲线在特定点的陡峭程度，并提供对函数行为的宝贵见解。为了更好地理解differential coefficient的重要性，让我们考虑一个涉及运动的实际例子。想象一辆汽车沿着一条直路行驶。汽车的位置可以用一个函数来描述，该函数将时间与距离联系起来。如果我们想知道汽车在某一时刻的速度，我们需要找到位置函数的differential coefficient。这使我们能够确定汽车的瞬时速度，这对于理解其运动至关重要。从数学上讲，differential coefficient被定义为当区间趋近于零时函数平均变化率的极限。这可以表示为：f'(x) = lim (h -> 0) [f(x + h) - f(x)] / h在这个公式中，f'(x)表示函数f在点x处的differential coefficient。变量h表示x的小变化，当h趋近于零时，我们获得该特定点的精确变化率。differential coefficient不仅仅是一个理论概念；它有许多实际应用。例如，在物理学中，它有助于计算加速度，即速度相对于时间的differential coefficient。在经济学中，它可以用来分析价格变化如何影响产品的需求。在生物学中，differential coefficient有助于建模人口增长率，使科学家能够根据当前数据预测未来的人口规模。此外，differential coefficient还有几何解释。它代表函数曲线在给定点的切线的斜率。通过理解这个斜率，我们可以直观地看到函数在局部的行为。如果differential coefficient为正，则函数在该点上升；如果为负，则函数在下降。如果differential coefficient等于零，则表示可能的最大值或最小值点，函数可能会改变方向。总之，differential coefficient是微积分中的一个重要概念，为函数行为提供了深刻的见解。无论是在物理、经济还是生物学中，它的应用都是广泛而多样的。通过理解differential coefficient，我们获得了一种强大的工具，用于分析变化并理解我们周围的世界。随着我们继续探索微积分的复杂性，differential coefficient的重要性无疑将继续成为数学分析的基石。