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...
Differentiation of Trigonometric FunctionsHere are the derivatives of trigonometric functions.If y = sin x, y' = cos x If y = cos x, y' = -sin x If y = tan x, y' = sec2 x If y = sec x, y' = sec x tan x If y = cosec x, y' = -cosec x cot x If y = cot x, ...
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...
g = exp(x)*cos(x); Differentiate the expressiong. y = diff(g) y =ex cos(x)−ex sin(x) To find the derivative ofgfor a given value ofx, substitutexfor the value usingsubsand return a numerical value usingvpa. Find the derivative ofgatx = 2. ...
比如:f(x)=sin(x)f(x)=sin(x), 要编程计算 diff(f, x)=cos(x) diff(f, x=5) = cos(5). 学习内容 Sympy 解析微分 数值微分:有限差分近似 (Finite Difference) 自动微分:科学计算与人工智能的交叉 (Auto Differentiation) 解析微分 需要使用计算机代数 (CAS), 又称“符号计算系统” 最著名的软件:...
g = exp(x)*cos(x); Differentiate the expressiong. Get y = diff(g) y =ex cos(x)−ex sin(x) To find the derivative ofgfor a given value ofx, substitutexfor the value usingsubsand return a numerical value usingvpa. Find the derivative ofgatx = 2. ...
Get y = diff(g) y = ex cos(x)−ex sin(x) To find the derivative of g for a given value of x, substitute x for the value using subs and return a numerical value using vpa. Find the derivative of g at x = 2. Get y_eval = vpa(subs(y,x,2)) ...
In the example of sin x2, the rule gives the result D(sin x2) = Dsin(x2) ∙ D(x2) = (cos x2) ∙ 2x. In the German mathematician Gottfried Wilhelm Leibniz’s notation, which uses d/dx in place of D and thus allows differentiation with respect to different variables to be ...
template <typename T>booloperator()(constT* theta,constT* t, T* residuals)const{constT q_0 =cos(theta[0]) * x[0] -sin(theta[0]) * x[1] + t[0];constT q_1 =sin(theta[0]) * x[0] +cos(theta[0]) * x[1] + t[1];constT r2 = q_0 * q_0 + q_1 * q_1; ...
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...