## xcrypt 3 years ago This is probably a weird question but is there a reason or intuition we write higher order derivatives as $\frac{d^n y}{dx^n}$ instead of $\frac{d^n y}{d^n x}$ or something similar?

1. thinker1

no man|dw:1352457865514:dw|

2. thinker1

do u understand mate

3. xcrypt

that's not what I am asking though

4. lgbasallote

do you agree that $\huge \frac{dy}{dx} = \frac d{dx}$ they're the same. right?

5. xcrypt

I have never the right hand side notation before

6. lgbasallote

you're not familiar with d/dx?

7. xcrypt

no

8. xcrypt

is it the same by definition?

9. lgbasallote

that's a bummer...i would assume you're at the start of your calculus class...hmm i'll try thinking of another analogy

10. xcrypt

I'm actually doing real analysis

11. lgbasallote

...then why are you not familiar with d/dx?

12. xcrypt

I have never seen it before, not in my books

13. xcrypt

But I've never taken calculus before ra so that might explain it

14. lgbasallote

hmm i can't think of any other way to explain the reason behind d^n y/dx^n without using d/dx...so i suppose i should explain that

15. thinker1

actually i wanted to show u that if $d ^{n}y /d ^{n} x$would have meant that its reciprocal had just an inverse relationship with it but actual $d ^{n}y /d ^{n} x$ is differently related to $d ^{n}x /d ^{n} y$

16. lgbasallote

$\frac{dy}{dx} = \frac d{dx}$ mainly because $\frac{dy}{dx} \implies \frac{d}{dx} (y)$ (this is algebra) then since y is usuallyimplied in functions, it is usually ommitted..that's why they just write d/dx for dy/dx

17. UnkleRhaukus

the derivative of a function is the rate that dependent variable changes as the independent variable varies in order

18. lgbasallote

then... let's say you want the second derivative...the second derivative would be $\frac d{dx} (\frac{dy}{dx})$ so again...using algebra, you get $\frac{d^2y}{dx^2}$ i don't know if that made anything clearer for you....

19. xcrypt

oh, we write f' or dy/dx instead of d/dx

20. lgbasallote

d/dx means derivative of with respect to x so dy/dx means derivative of y with respect to x

21. xcrypt

ah ok

22. UnkleRhaukus

$y=x^2$$\frac{\text dy}{\text dx}=2x$$\frac{\text d^2y}{\text dx^2}=2$ $\frac{\text d^2y}{\text dx}=2\text dx$${\text d^2y}=2\text dx{\text dx}$${\iint \text d^2y}=2\iint\text dx^2$$\int \text dy=2\int( x+c)\text dx$$y=2\frac{x^2}2+c$$y={x^2}+cx+d$