Question

how can I prove that d/dx (1/y) = 0. ??? how can I prove that d/dx (1/y) = 0. ??? @MIT 18.01 Single …

Answer 1

d/dx of 1/y = -1/y2 not 0, I do not know if you can prove it to be 0.

Answer 2

why is it occurring?

Answer 3

if I put d/dx of 1/y in MS math or wolfram it return 0

Answer 4

First of all
\[ \frac{d \ }{dx} (1/x) = -\frac{1}{x^2} \]

Now, if y is a function of x, y = y(x), then using implicit differentiation and the chain rule,
\[ \frac{d \ }{dx} (1/y) = -\frac{1}{y^2} \frac{dy}{dx} \]

But if \(y\) is just a constant, completely unrelated to \(x\), then \(1/y\) is also just a constant (assuming of course that \(y\) is not zero), and for any constant \(c\)
\[ \frac{d \ }{dx} c = 0 \]

Answer 5

The reason Wolfram is giving you that (d/dx) of 1/y is zero is it is treating y as a constant, unrelated to x.

That may be correct, depending on your context. But very often we are treating y as the vertical graphing variable and y is dependent on x, as y = f(x). In this case, the derivative is most emphatically not zero, as I just showed above.