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Replacement of a variable only for a part of an expression

You may either use ReplacePart (close to what @Alrubaie proposed) expr = a^2 + f[a]; ReplacePart[expr, 2 -> f[c]] (* a^2 + f[c] *) or map the replacement ...
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Replacement of a variable only for a part of an expression

You just need ReplacePart Where ReplacePart[Function/Expression , Location which part to replace] ...
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A complicated derivative problem

You have a precedence problem. Look at "tutorial/OperatorInputForms" in the help. You will find that "/." has a higher precedence than "//". Therefore, what you evaluate ...
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Transform rational equations to polynomial equations

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CellObject[Number] to its content

NotebookRead gives the cell expression (see the first example in the docs for CellObject); ...
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Parsing an expression for coefficients and more

Another way, as the comment @Henrik Schumacher said: ...
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Parsing an expression for coefficients and more

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Parsing an expression for coefficients and more

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