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It seems very basic but I can't understand...

Consider $f(x)=2x$. I want to differentiate $L=(x-f(x))b + 3(f(x))$ regarding $f(x)$.

When I looked at the solution, it says $\partial L/\partial f = -b+3$.

But I am confused because I can't get why $x$ is simply considered a constant and ignored. Shouldn't it be $$ (dx/df - 1)b+3 = (1/2-1)b+3=-b/2+3? $$ Please help me out. Thank you!

Ernie060
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jennings
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1 Answers1

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$\partial L/\partial f $ means that it is partial derivative and therefore, treating any other variable as a constant. Therefore, in this case, $x$ will be treated as a constant and $\frac{\partial x}{\partial y} = 0.$

Your answer will be right if the question was asking $$\frac{d L}{d f} $$

underdisplayname
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