how to calculate a derivative

can some one guide me how to calculate a derivative and integration in matlab . can you please give a little example.

[Jan]

Symbolically or numerically?

Answer 1

[bym]

Symbolically

syms x real
f = 1/x
int(f,1,2)  % integration

ans =

log(2)

diff(f)  %differentiation
ans =

 -1/x^2

[edit - amplification]

syms x a b real positive
f = 1/x

f =

1/x

int(f) % without limits

ans =

log(x)

int(f,a,b) % with limits

ans =

log(b) - log(a)

fn  = matlabFunction(f) % convert symbolic to anonymous function

fn = 

      @(x)1./x

quadgk(fn,1,2) % integrate numerically

ans =

      0.6931

log(2)  % previous result from symbolic integration

ans =

      0.6931

   (fn(2+1e-6)-fn(2))/1e-6  %numerical derivative at fn(2)

ans =

     -0.2500

   subs(diff(f),2) %substitute 2 into symbolic result previously obtained

ans =

     -0.2500

[Nasir Qazi]

inside int(f,1,2) what exactly this 1,2 stand for in here. 2ndly what do you means by symbolically of numerically .?, right and wht if we have limits in integration, how can we solve that expression .?

[Walter Roberson]

int(f,1,2) is integrate the symbolic expression f over the definite interval from 1 to 2.

[Nasir Qazi]

in case of limits in integration then ?

[Jan]

Yes, Nasir, then the integral is calculated from 1 to 2. "Symbolically" mean calculations with symbols, usually characters. The result is a formula. "Numerically" means, that you calculate a numerical value, a number.

[Sergio E. Obando]

Just here to suggest some recent resources, There is a nice section in the Symbolic Math Toolbox with additional examples for differentiation as well as a FEX curriculum on this topic:

Answer 2

[Magdalena Glinska]

f = @(x) sin(x);
second_derivative_f = matlabFunction(diff(sym(f)));

Answer 3

[Hamza saeed khan]

syms x
f = x;
diff(f,x)

why this code give me error as;

>>Error in diff (line 1)

syms x

[Dheeresh agarwal]

diff(f,1)

[Walter Roberson]

You probably do not have the symbolic toolbox installed or licensed.

Also, you accidentally named your script diff.m which is going to conflict with calling diff() to differentiate.

Answer 4

[Achimsettythanmay]

syms x real
f = 1/x

f = 

int(f,1,2) % integration

ans = 

diff(f) %differentiation

ans =