No, it's better to use the uppercase letters for the dependent variables and lowercase letters for their corresponding independent variables, because then it's easier to track which one depends on which. Using f(x) would be more confusing. However, I have a bigger issue with this notation: that you use primes and double-primes for derivatives. Yes, I know, if they don't depend on any other variable, they're just ordinary derivatives (of a single variable), so it's not that much of a problem. But primes hide with respect to which independent variable are we differentiating. I'd rather use subscripted independent variables to make it clear (if you want to avoid Leibniz notation that much). Otherwise students might get confused and differentiate with respect to a wrong variable.
thank you very much, you are a hero !!
sir why is the function of x sine?
What does X(x) mean?
X(x) means X is a function of x. I could have instead used f(x) and get the same answer.
No, it's better to use the uppercase letters for the dependent variables and lowercase letters for their corresponding independent variables, because then it's easier to track which one depends on which. Using f(x) would be more confusing.
However, I have a bigger issue with this notation: that you use primes and double-primes for derivatives. Yes, I know, if they don't depend on any other variable, they're just ordinary derivatives (of a single variable), so it's not that much of a problem. But primes hide with respect to which independent variable are we differentiating. I'd rather use subscripted independent variables to make it clear (if you want to avoid Leibniz notation that much). Otherwise students might get confused and differentiate with respect to a wrong variable.