Phrase
partial derivative
偏导数
a derivative of a function of several variables with respect to one variable, treating the other variables as constants
- 1.
A derivative with respect to one variable of a function of several variables with the other variables held constant.
多变量函数关于其中一个变量的导数,其他变量保持不变。
多变量函数关于其中一个变量的导数,其他变量保持不变。；偏微商
In use
In multivariable calculus, the partial derivative of f with respect to x measures how f changes as x varies while y is held constant.
To find the rate of change of temperature along the x-axis, we compute the partial derivative of the temperature function with respect to x.
Economists often use the partial derivative to analyze the marginal effect of one input while keeping other inputs fixed.
partial derivative of [function] with respect to [variable]
The partial derivative of f(x,y) with respect to x is denoted ∂f/∂x.
函数f(x,y)关于x的偏导数记作∂f/∂x。
take the partial derivative of [function] with respect to [variable]
To find the gradient, take the partial derivative of each variable.
为求梯度，对每个变量取偏导数。
compute the partial derivative(s) of [function]
We computed the partial derivatives of the cost function.
我们计算了成本函数的偏导数。
Common mistakes
We need to compute the part derivative of z with respect to y.We need to compute the partial derivative of z with respect to y.
中文'偏导数'中的'偏'对应partial，而'部分'是part，学生容易直译导致错误。
The partial derivative of f to x is 2x.The partial derivative of f with respect to x is 2x.
中文表达'关于x的偏导数'，学生可能误用介词'to'代替'with respect to'。
Connections
Confusing words
- ordinary derivative
- 常导数 · 偏导数用于多元函数，对其中一个变量求导时固定其他变量；常导数用于单变量函数。
- total derivative
- 全导数 · 偏导数仅考虑一个变量的变化，而全导数考虑所有变量同时变化时函数的总体变化率。
Word family
- partial
- 部分的；偏的 · adjective
- partially
- 部分地 · adverb
- derivative
- 导数 · noun
- derive
- 推导；导出 · verb
Learner notes
Grammar Note
数学术语，用于微积分中，表示多元函数关于一个变量的导数，其他变量视为常数。
Learn the forms together
页面下方列出了常见词形变化。学习时注意它们在句子中的语法位置。
Dictionary facts from ECDICT, WIKTIONARY.