Why don't equivalence transformations preserve derivatives?

Asked Jul 06 '21 at 12:38

Active Jul 06 '21 at 12:38

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I have a very simple question I'm unable to answer.

I have calculated the following derivative

$$ \frac{0.56}{x^2} = 0.42$$

The next derivative is

$$ 0 - \frac{1.12}{x^3} = 0$$

However If I take the first derivative and transform it to

$$ 0.56 = 0.42 * x^2$$

The next derivative is:

$$2*0.42*x => 0.84x$$

So equivalence transformations are not allowed when handling derivatives? I'm sorry If this question is at a very low level.

asked Jul 06 '21 at 12:38

CuriousIndeed

2

I am completely lost here. what do you mean exactly by "I have calculated the following derivative" and then writing down an equation? – alphaomega Jul 06 '21 at 12:41
2

You're far from the first person to have noticed this. See taking the derivative of both sides of an equation. – Toby Mak Jul 06 '21 at 12:42
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Does this answer your question? Is differentiating on both sides of an equation allowed?. In short, you need both functions to be equal to each other for all values of $x$, rather than only for certain values of $x$. – Toby Mak Jul 06 '21 at 12:44
So basically when handling derivatives the safe way is to bring all the terms on one side and then take the derivative? – CuriousIndeed Jul 06 '21 at 13:03

0 Answers0