用implicit differentiation求得:y’ = 1/cos y 精彩部分:进一步转化为:y’ = 1/√[1-(sin y)^2] 而sin y = x,因此,(sin y)^2 = x^2, 解出:y’ = 1/√(1-x^2) 书本内容: 第一,书本对反函数进行了进一步的解释(补充高中知识欠缺的我)。 Theorem 5.6 Reflective property of inverse functi...
当x\neq 0 时利用链式法则来求导,得到: \begin{aligned}f^\prime(x) = 2x\sin\frac{1}{x}- \cos\frac{1}{x}\end{aligned}。 当x=0 时,不能利用链式法则,因为这个时候 \begin{aligned}\frac{1}{x}\end{aligned} 没定义,我们利用导数定义来计算: \begin{aligned}\lim\limits_{x\to 0}\frac...
TheGroupwillcontinuetoimplementthestrategiesofdifferentiationandcostleadershipinthesecond halfoftheyear,seekingtopursuestabledevelopmentanddeliversoundresultsbyenhancingprojectbasedoperationsandextendingitsadvantagesincostandtechnologyaswellasitsabilityinone-stop project delivery. ...
32 -- 6:12 App 4.3 Differentiation - Trig. functions sin(x), cos(x) and tan(x) 17 -- 10:00 App 4.21 Tangents to Implicit Curves 15 -- 6:04 App P3 4.20 Differentiation _ Implicit Equations (Using the Product Rule)友情提示:为了您的体验,点击作品信息、UP主个人空间、点赞、收藏、转发...
Polar coordinates are used when data concerning position are received in the form of distance and direction, or, as the armed services would say, range and bearing. An instrument such as a radar scanner automatically measures r and θ. The definitions of cos θ and sin θ presented in the ...
(x). In words, the first factor on the right,Df(g(x)), indicates that thederivativeofDf(x) is first found as usual, and thenx, wherever it occurs, is replaced by the functiong(x). In the example of sinx2, the rule gives the resultD(sinx2) =Dsin(x2) ∙D(x2) = (cosx2...
Example 2: Find the differentiation of y = cos(tan x) Solution: Given: y = cos(tan x) We differentiate y with respect to x. Let u = tan x y = cos u Using the chain rule of differentiation, dy/dx = dy/du . du/dx dy/dx = d(cos u)/du . d(tan x)/dx = -sin u . ...
微分，尤其是导数，描述了一个函数在某一个点的瞬时变化率，这个概念之所以重要，是因为她可以在动态系统...
Given that {eq}\displaystyle f(x,y) {/eq} is differential at {eq}\displaystyle (3,8) {/eq} with: {eq}\displaystyle \lim_{(x,y) \to (3,8)} = 7, \ f_x (3,8)=-4 {/eq} and {eq}\displays...
twice with respectt to x gives us the original thing plus a factor of -α2, and for T we have something that when differentiated twice with respect to t gives us the original plus a factor of -α2c2. The only way we can get these is with sin or cos functions, so the options ...