MATLAB符號運算--求導diff

diff

Differentiate symbolic expression

求符號表達式的微分

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 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) 求一個符號表達式 expr相對於由symvar肯定的自由變量的微分。

Examples

Differentiate the following single-variable expression one time:

  
  
           
  
  

   
   
            
   
   

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

The result is

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

Differentiate the following single-variable expression six times:

  
  
           
  
  

   
   
            
   
   

     syms t; 
    
diff(t^6,6) 
   
  
  
           
  
  

The result is

ans =
720

Differentiate the following expression with respect to t:

  
  
           
  
  

   
   
            
   
   

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

The result is

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

綜合應用

給定函數f(x)=cosx/(x ³+7x+2)的一階導數，並將每一個點上的值與原函數的值經過matlab函數繪製出來.

1. 一階導數

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

   pretty(f1d)
2. 繪製原函數以及求導後函數曲線

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