Easy SMH Question (1 Viewer)

[Ambility]

Could someone show me how to do this?

 

[KingOfActing]

Could someone show me how to do this?

Treat it the derivative as a fraction:



Now integrate both sides:



Now just substitute the information given to find the constant = 0, so when x = 2



EDIT: If you don't feel comfortable with using non-standard analysis to treat the derivative as a quotient of infinitesimals rather than an operator, just recall that which can be proven with inverse functions. Then using that you get

 

[InteGrand]

Could someone show me how to do this?

Edit: Done above.

(Btw, it's SHM rather than SMH, unless you were referring to Sydney Morning Herald or something rather than Simple Harmonic Motion, which is quite possible since this question isn't a SHM one.)

 

[Ambility]

Thank you both very much. I hate that I have been taught up until now that the derivative is just an operator or symbol. Only now must I use it as a quotient of infinitesimals as KingofActing said. On that note, why do you get t when you integrate dt?

 

[InteGrand]

Thank you both very much. I hate that I have been taught up until now that the derivative is just an operator or symbol. Only now must I use it as a quotient of infinitesimals as KingofActing said. On that note, why do you get t when you integrate dt?

∫ dt = ∫ 1 dt = t + C.

 

[Nailgun]

Isn't this just like if dy/dx = f(x) then dx/dy = 1/f(x)?


edit: jks i think thats what KoA said at the end of his thingo

 

[InteGrand]

Isn't this just like if dy/dx = f(x) then dx/dy = 1/f(x)?

It's essentially the technique of separation of variables for solving an ordinary differential equation: https://en.wikipedia.org/wiki/Separation_of_variables#Ordinary_differential_equations_.28ODE.29 .