Derivate using chain rule doesn't work in MATLAB

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Siva Mokkapati 2020-11-8

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评论： Star Strider 2020-11-11

I am trying to derive the gradient and hessian for a given function. When i directly do the gradient it works well but when I apply chain rule it doesn't works and throws me an error as below

Error using sym/diff (line 70)
Second argument must be a variable or a nonnegative integer specifying the number of differentiations.
Error in EO_a1 (line 12)
dfr = diff(f(x),r(x));
%My MATLAB Code
syms x a b const r(x)
const = (a*x);
r(x) = (const - b);
f(x) = (1/2)*(r(x)^2);
gradient = diff(f(x));
gradient;
hessian = diff(gradient);
hessian;
%gradient applying the chain rule
dfr = diff(f(x),r(x));
dfr;
drx = diff(dfr,x);
drx;

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Answer 1

Star Strider 2020-11-8

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This works for me:

syms f(x) r(x) x 
dfr = diff(f(x)*r(x))

producing:

dfr =
f(x)*diff(r(x), x) + r(x)*diff(f(x), x)

that to me appears to bear a strong resemblance to the chain rule for the product of two functions.

I have no idea what you are doing in the last part of your Question.

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Siva Mokkapati 2020-11-11

Thanks for your response Star Strider.

I have calcuted the 'Gradient' directly in the inital code and in the last part I am trying to calculte gradient using chain rule. (df/dr)*(dr/dx). Ideally both these results should be same. but your suggestion above is giving me completely different answer.

Star Strider 2020-11-11

My pleasure!

There is a gradient and a hessian function in the Symbolic Math Toolbox (both introduced in R2011b).

They may be what you want. (Unless you are not allowed to use them if this is a homework assignment. You can nevertheless use them to check the results of your code.)

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