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好学高数(四):导数与微分

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今天小编为大家带来的是好学高数(四):导数与微分

Share interests, spread happiness, increase knowledge, and leave a good future! Dear you, this is LearningYard New Academy. Today, the editor brings you a studious high number (4): derivatives and differentiation.

一、高阶导数

01高阶导数求导公式

02幂指函数(底数与指数均为函数)

求导方法:将底数(指数)看为常数后求导,再对被看成常数的函数求导,二者相乘。之后再加上指数(底数)看为常数后求导,再对被看成常数的函数求导,二者相乘。

Derivation method: take the base (exponent) as a constant and then derive the function that is regarded as a constant, and multiply the two. Then add the exponent (base) as a constant and then derive, and then derive the function that is regarded as constant, and multiply the two.

例如:

二、隐函数求导

01隐函数的导数

适用对象:无法将y单独分离到一侧

使用方法:等号两侧同时求导

Applicable object: It is not possible to separate y to one side alone Use method: Derive on both sides of the equal sign at the same time

02 参数方程所确定的导数

一阶导数:

二阶导数:

(当分子分母有一堆相乘时取对数)

(Take the logarithm when the numerator denominator has a bunch of multiplications)

三、微分的基本运算

01微分法则

微分表达式:dy=f'(x)△x

(基本还是掌握函数的求导)

Differential expression: dy=f'(x)△x (basic or mastering the derivation of functions)

END

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翻译:谷歌翻译
参考:《高等数学》第七版上册 同济大学数学系、百度
声明:本文由LearningYard新学苑原创,若有侵权请联系删除!


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