MATLAB 求导diff

diff

Differentiate symbolic expression_r_r

求符号表达式的微分

Syntax

diff(expr)

diff(expr, v)

diff(expr, sym(‘v’))

diff(expr, n)

diff(expr, v, n)

diff(expr, n, v)

Description

diff(expr) differentiates a symbolic expression_r_r expr with respect to its free variable as determined by symvar.

diff(expr, v) and diff(expr, sym(‘v’)) differentiate expr with respect to v.

diff(expr, n) differentiates expr n times. n is a positive integer.

diff(expr, v, n) and diff(expr, n, v) differentiate expr with respect to v n times.

diff(expr) 求一个符号表达式expr相对于由symvar确定的自由变量的微分。

Examples

Differentiate the following single-variable expression_r_r one time:

syms x;
diff(sin(x^2))

The result is

ans = 2*x*cos(x^2)

Differentiate the following single-variable expression_r_r six times:

syms t;
diff(t^6,6)

The result is

ans = 720

Differentiate the following expression_r_r with respect to t:

syms x t;
diff(sin(x*t^2), t)

The result is

ans = 2*t*x*cos(t^2*x)

综合应用

给定函数f(x)=cosx/(x3+7x+2)的一阶导数，并将每个点上的值与原函数的值通过matlab函数绘制出来.

subs用法见http://blog.sina.com.cn/s/blog_4b94ff130100gdk9.html

一阶导数

syms x;
f=cos(x)/(x^3+7*x+2);
f1d=diff(f,x)
pretty(f1d)

绘制原函数以及求导后函数曲线

x1=0:0.001:5;
y=subs(f,x,x1);
y1d=subs(f1d,x,x1);
plot(x1,y,x1,y1d,':')