一阶导数英语怎么说及英文翻译

『壹』 微积分里面专有名词中英文对照

absolutely convergent 绝对收敛
absolute value 绝对值
algebraic function 代数函数
analytic geometry 解析几何
antiderivative 不定积分
approximate integration 近似积分
approximation 近似法、逼近法
arbitrary constant 任意常数
arithmetic series/progression (AP)算数级数
asymptotes (vertical and horizontal)(垂直/水平)渐近线
average rate of change 平均变化率
base 基数
binomial theorem 二项式定理，二项展开式
Cartesian coordinates 笛卡儿坐标(一般指直角坐标)
Cartesian coordinates system 笛卡儿坐标系
Cauch’s Mean Value Theorem 柯西均值定理
chain rule 链式求导法则
calculus 微积分学
closed interval integral 闭区间积分
coefficient 系数
composite function 复合函数
conchoid 蚌线
continuity (函数的)连续性
concavity (函数的)凹凸性
conditionally convergent 有条件收敛
continuity 连续性
critical point 临界点
cubic function 三次函数
cylindrical coordinates 圆柱坐标
decreasing function 递减函数
decreasing sequence 递减数列
definite integral 定积分
derivative 导数
determinant 行列式
differential coefficient 微分系数
differential equation 微分方程
directional derivative 方向导数
discontinuity 不连续性
discriminant (二次函数)判别式
disk method 圆盘法
divergence 散度
divergent 发散的
domain 定义域
dot proct 点积
double integral 二重积分
ellipse 椭圆
ellipsoid 椭圆体
epicycloid 外摆线
Euler's method (BC)欧拉法
expected valued 期望值
exponential function 指数函数
extreme value heorem 极值定理
factorial 阶乘
finite series 有限级数
fundamental theorem of calculus 微积分基本定理
geometric series/progression (GP)几何级数
gradient 梯度
Green formula 格林公式
half-angle formulas 半角公式
harmonic series 调和级数
helix 螺旋线
higher derivative 高阶导数
horizontal asymptote 水平渐近线
horizontal line 水平线
hyperbola 双曲线
hyper boloid 双曲面
implicit differentiation 隐函数求导
implicit function 隐函数
improper integral 广义积分、瑕积分
increment 增量
increasing function 增函数
indefinite integral 不定积分
independent variable 自变数
inequality 不等式
ndeterminate form 不定型
infinite point 无穷极限
infinite series 无穷级数
infinite series 无限级数
inflection point (POI) 拐点
initial condition 初始条件
instantaneous rate of change 瞬时变化率
integrable 可积的
integral 积分
integrand 被积分式
integration 积分
integration by part 分部积分法
intercept 截距
intermediate value of Theorem ：中间值定理
inverse function 反函数
irrational function 无理函数
iterated integral 逐次积分
Laplace transform 拉普拉斯变换
law of cosines 余弦定理
least upper bound 最小上界
left-hand derivative 左导数
left-hand limit 左极限
L'Hospital's rule 洛必达法则
limacon 蚶线
linear approximation 线性近似法
linear equation 线性方程式
linear function 线性函数
linearity 线性
linearization 线性化
local maximum 极大值
local minimum 极小值
logarithmic function 对数函数
MacLaurin series 麦克劳林级数
maximum 最大值
mean value theorem (MVT)中值定理
minimum 最小值
method of lagrange multipliers 拉格朗日乘数法
molus 绝对值
multiple integral 多重积分
multiple 倍数
multiplier 乘子
octant 卦限
open interval integral 开区间积分
optimization 优化法，极值法
origin 原点
orthogonal 正交
parametric equation (BC)参数方程
partial derivative 偏导数
partial differential equation 偏微分方程
partial fractions 部分分式
piece-wise function 分段函数
parabola 抛物线
parabolic cylinder 抛物柱面
paraboloid ：抛物面
parallelepiped 平行六面体
parallel lines 并行线
parameter ：参数
partial integration 部分积分
partiton ：分割
period ：周期
periodic function 周期函数
perpendicular lines 垂直线
piecewise defined function 分段定义函数
plane 平面
point of inflection 反曲点
point-slope form 点斜式
polar axis 极轴
polar coordinates 极坐标
polar equation 极坐标方程
pole 极点
polynomial 多项式
power series 幂级数
proct rule 积的求导法则
quadrant 象限
quadratic functions 二次函数
quotient rule 商的求导法则
radical 根式
radius of convergence 收敛半径
range 值域
(related) rate of change with time (时间)变化率
rational function 有理函数
reciprocal 倒数
remainder theorem 余数定理
Riemann sum 黎曼和
Riemannian geometry 黎曼几何
right-hand limit 右极限
Rolle's theorem 罗尔(中值)定理
root 根
rotation 旋转
secant line 割线
second derivative 二阶导数
second derivative test 二阶导数试验法
second partial derivative 二阶偏导数
series 级数
shell method (积分)圆筒法
sine function 正弦函数
singularity 奇点
slant 母线
slant asymptote 斜渐近线
slope 斜率
slope-intercept equation of a line 直线的斜截式
smooth curve 平滑曲线
smooth surface 平滑曲面
solid of revolution 旋转体
symmetry 对称性
substitution 代入法、变量代换
tangent function 正切函数
tangent line 切线
tangent plane 切(平)面
tangent vector 切矢量
taylor's series 泰勒级数
three-dimensional analytic geometry 空间解析几何
total differentiation 全微分
trapezoid rule 梯形(积分)法则

『贰』 微积分英文专业术语

下面提供AP最常用的微积分词汇，如果需要翻译，请Hi我：
antiderivative 原函数
a representation, usually in symbolic form, of any function whose derivative is a given function.

tangent 切线，斜率，正切
a line or a plane that touches a curve or a surface at a single point.

chain rule 链式求导法
the theorem that defines the method for taking the derivative of a composite function.

concave downward 向下开口
part of a graph resembling an upside down bowl.

concave upward 向上开口
part of a graph resembling a right side up bowl.

continuous 连续
being in immediate connection or spatial relationship.

critical point 临界点
point on the graph where the derivative is either 0 or undefined.

cylindrical shell method 旋转体积圆筒积分法
technique for finding the volume of a solid of revolution.

definite integral 定积分
the representation of the difference in values of a primitive of a given function evaluated at two designated points.

derivative 导数，求导，导函数
the change of a function with respect to an infinitesimally small change in the independent variable, or the slope of the point's tangent line.

differentiable 可导的，可微的
a function whose graph is curve that is smooth and contains no discontinuities or cusps.

disk method 旋转体积圆盘法
technique for finding the volume of a solid of revolution when integrating along the axis of revolution.

extreme value theorem 极值理论
guarantees an absolute max and an absolute min

first derivative test 极值点、拐点的确定法
determines whether an inflection point is a minimum, maximum, or neither.

higher order derivatives 高阶导数，高阶导函数
any derivatives beyond the first derivative.

implicit differentiation 隐函数求导、微分
method for finding the derivative of an implicitly defined function or relation using the chain rule.

indefinite integral 不定积分
another way of saying antiderivative.

instantaneous rate of change 瞬时牵连变化率、相关变化率
rate of change at a particular moment.

instantaneous velocity 瞬时速度
rate at which an object is moving at a particular moment.

integration by parts 分部积分
a method of evaluating an integral by use of the formula, ∫udv = uv − ∫v.

limit 极限
value that a function approaches as the domain variable approach a specific value.

mean value theorem 中值定理
the theorem that there is a point in a continuous curve where the derivative is equal to the average derivative of the entire arc.

normal line 法线
line that is at a 90 degree angle, perpendicular to a surface.

point-slope form 直线方程点斜式
form used the most when finding the equation of a line.

riemann sum 黎曼积分
method for approximating the definite integral.

second derivative test 用二阶导数检查是否是极大值点或极小值点
determines whether a critical point is a relative minimum or maximum using the value of the second derivative at the point.

u-substitution U型变量代换
integration method that involves using the chain rule in reverse.

trigonometric substitution 三角函数变量代换
substitution of trigonometric functions for other expressions to eliminate radicals in integrals.

washer method 旋转体积的圆筒积分法
similar to the disk method but using washers instead of disks.

『叁』 求微积分的英语词汇,

你好,本人现在在美国读高中正在学微积分,所以微积分的专业词汇英文知道的比较多一些 如果中文有翻译不对的希望你能理解
微积分 Calculus
极限 limit
积分 integration
微分 differentiation
导数 derivative
极值应该是extrema
三角函数 trig(trigonometric) functions
反三角函数 inverse trig(trigonomic) functions
微分方程 differential equations
黎曼积分 Riemann Sums
定积分 definite integrals
指数函数 exponential functions
对数函数 log(logarithmic) functions
自然对数函数 natural log functions
微积分基本定理 the Fundamental Theorem of Calculus
洛必达法则 l'hopital's rule
Rolle定理 Rolle's Theorem
u代入法 u substitution
弧线长度 arc length
正无穷大 positive infinity
负无穷大 negative infinity

例题
1. Find the volume of the solid formed by revolving the region by the graphs of y = x^2 +1, y = 0, and x = 1. About the y-axis.
求被函数y= x^2 +1, y = 0,和 x = 1所包围的区域围绕Y轴旋转后形成的体积.
答案是3pi/2

2.Find the area bounded by the graphs of x =3 - y^2 and x = y + 1.
求被x = 3 - y^2 和 x = y + 1 的图像所包围的面积.
答案是9/2

3.A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the page are to be 3/2 inches, and the margins on the left and right are to be 1 inch. What should the dimensions of the page be so that the least amount of paper is used?
有一页长方形的纸,上面有24平方英寸的印刷区域,纸上端和下端的空白都是3/2英寸,左边和右边的空白都是1英寸.求这张纸的长宽以使所用的纸最少.

我知道这些不是很多只是微积分的一小部分,不过也是费了好大力气写的希望能对你有帮助吧!