matlab求函数y=x∧3+2sin(x∧2-x)+cos(x-5)的一阶导数和二阶导数

函数y=x^3 * 2sin(x^2-x) * cos(x-5)的一阶导数为：
y' = 3x^2 * 2sin(x^2-x) * cos(x-5) + x^3 * 2cos(x^2-x) * (2x-1) * cos(x-5) - x^3 * 2sin(x^2-x) * sin(x-5)

函数y=x^3 * 2sin(x^2-x) * cos(x-5)的二阶导数为：
y'' = 6x * 2sin(x^2-x) * cos(x-5) + 6x^2 * cos(x^2-x) * cos(x-5) - 6x^2 * sin(x^2-x) * sin(x-5) + x^3 * 2cos(x^2-x) * (-2x+3) * cos(x-5) - x^3 * 2sin(x^2-x) * cos(x-5) * (2x-1)

相关问题

matlab求函数y=x∧3+2sin(x∧2-x)+cos(x-5)的一阶导数和二阶导数的代码

syms x;
y = x^3 * 2*sin(x^2 - x) * cos(x - 5);
dy = diff(y, x);
d2y = diff(dy, x);
disp("一阶导数：");
disp(dy);
disp("二阶导数：");
disp(d2y);

这是求函数y=x∧3 2sin(x∧2-x) cos(x-5)的一阶导数和二阶导数的 MATLAB 代码。

使用matlab求f(x)＝(sin x)/x²＋4x＋3的一阶导数，二阶导数和三阶导数

可以使用符号计算工具箱中的diff函数来求函数的导数。具体操作如下：

首先定义函数f(x)：

syms x;
f(x) = sin(x)/(x^2+4*x+3);

求一阶导数：

diff(f,x)

输出结果为：

cos(x)/(x^2 + 4*x + 3) - (2*x + 4)*sin(x)/(x^2 + 4*x + 3)^2

求二阶导数：

diff(f,x,2)

输出结果为：

-(2*cos(x)*(2*x + 5))/(x^2 + 4*x + 3)^2 + (6*sin(x)*(2*x + 5))/(x^2 + 4*x + 3)^3 - (2*sin(x))/(x^2 + 4*x + 3) + (8*x + 16)*sin(x)/(x^2 + 4*x + 3)^2 - (2*cos(x)*(2*x + 4))/(x^2 + 4*x + 3)^2

求三阶导数：

diff(f,x,3)

输出结果为：

(10*cos(x)*(2*x + 5))/(x^2 + 4*x + 3)^3 - (36*sin(x)*(2*x + 5))/(x^2 + 4*x + 3)^4 + (6*cos(x)*(2*x + 5))/(x^2 + 4*x + 3)^2 - (32*x - 72)*cos(x)/(x^2 + 4*x + 3)^3 + (2*sin(x)*(4*x + 8))/(x^2 + 4*x + 3)^2 - (24*x - 48)*sin(x)/(x^2 + 4*x + 3)^3

因此，f(x)的一阶导数为cos(x)/(x^2 + 4*x + 3) - (2*x + 4)*sin(x)/(x^2 + 4*x + 3)^2，二阶导数为-(2*cos(x)*(2*x + 5))/(x^2 + 4*x + 3)^2 + (6*sin(x)*(2*x + 5))/(x^2 + 4*x + 3)^3 - (2*sin(x))/(x^2 + 4*x + 3) + (8*x + 16)*sin(x)/(x^2 + 4*x + 3)^2 - (2*cos(x)*(2*x + 4))/(x^2 + 4*x + 3)^2，三阶导数为(10*cos(x)*(2*x + 5))/(x^2 + 4*x + 3)^3 - (36*sin(x)*(2*x + 5))/(x^2 + 4*x + 3)^4 + (6*cos(x)*(2*x + 5))/(x^2 + 4*x + 3)^2 - (32*x - 72)*cos(x)/(x^2 + 4*x + 3)^3 + (2*sin(x)*(4*x + 8))/(x^2 + 4*x + 3)^2 - (24*x - 48)*sin(x)/(x^2 + 4*x + 3)^3。