Derivatives for Backprop

Hi, can someone explain to me how we got derivative -1/4 for the last example in the derivatives video.

If J(w) = 1/w, then how do we get to -1/4. Is this the quotient rule? Or perhaps this is the power rule applied to fractions? Where did the negative come from?

I understand how we got to that answer arithematically with epsilon as J(w) = 1/2.001, but can we quickly calculate this with a power or quotient rule like in the previous examples?

It’s always helpful if you include the video title and a time mark.

Are you referring to this slide?

Assuming that’s the example you’re asking about:
It’s the power rule.
The cost equation is J(w) = 1/w.
That’s equivalent to J(w) = w^{-1}
The power rule says the derivative of x^n is nx^{n-1}.
So that becomes -1w^{(-1-1)}, or -1/w^{2}

Substitute w=2 and you’re done.


Ok, I got it, thank you.