cderivative
Derivative of a univariate, vectorvalued function using the central difference approximation.
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Contents
Syntax
df = cderivative(f,x0) df = cderivative(f,x0,h)
Description
df = cderivative(f,x0) numerically evaluates the derivative of with respect to at using the central difference approximation with a default relative step size of , where is the machine zero.
df = cderivative(f,x0,h) numerically evaluates the derivative of with respect to at using the central difference approximation with a userspecified relative step size .
Input/Output Parameters
Variable  Symbol  Description  Format  
Input  f  univariate, vectorvalued function ()  1×1 function_handle 

x0  evaluation point  1×1 double 

h  (OPTIONAL) relative step size  1×1 double 

Output  df  derivative of with respect to , evaluated at  m×1 double 
Note
 This function requires 2 evaluations of .
 If the function is scalarvalued, then .
Example #1: Derivative of a scalarvalued function.
Approximate the derivative of at using the cderivative function, and compare the result to the true result of .
Approximating the derivative,
f = @(x) x^3; df = cderivative(f,2)
df = 12.0000
Calculating the error,
error = df12
error = 3.3153e10
Example #2: Derivative of a vectorvalued function.
Approximate the derivative of
at using the cderivative function, and compare the result to the true result of
Approximating the derivative,
f = @(t) [sin(t);cos(t)]; df = cderivative(f,1)
df = 0.5403 0.8415
Calculating the error,
error = df[cos(1);sin(1)]
error = 1.0e10 * 0.1420 0.1959