/sci/ - Science & Math

>>16230379
>A function of x is linear if you can write it as a polynomial where every appearance of x is without an exponent (i.e. x1)
Yes. When I said you account for Δx more than once I was kinda trying to state "this is what happens when you have an exponent and why its derivative increases" in a very loose way.
>Don't mix them up.
Sorry if I do. I'll look that up.
>>16230380
I know. I started ages ago comparing
x^2 + Δx^2 =/= (x+Δx)^2
I just wanted to know why (x+Δx)^2 yields a higher number. This led to 2xΔx + Δx^2 and the whole story.
>does 1/2 + 1/3 = 1/5?
No. When I started with 1/x I did the same thing as above and long story short it's all the same stuff related to "what is this function exactly telling me to do"?
>Why not just explain it easier
Sorry I try. When I ask why is 1/x non-linear, I assume the other end takes for granted that every derivate has its own logical explanation, just like you can deduce why the derivate of sin(x) is cos(x) by looking at the unit circle.
I was asking, what does 1/x actually mean to have a decreasing derivative? I did the thing algebraically and geometrically and I literally don't know what to call this anymore because every time I say derivative this happens.