Distribution?

[Wolverine]

Hello, everyone!
Sorry about the banal question, but I have a doubt. .

if I have a function y(t)=a * sin(x) where a constant

if x is function of time, i.e. x=x(t), how much the derivative of y respect applies
in time?

Thank you! !

 

[maxopus]

But if x is the function of time, it would no longer be correct to write x=f(t) if it is so the derivative first you should be able to get it easily.

 

[Fulvio Romano]

df/dx is the derivative of f depending on x

in general if I have a f(g(x)) I can write that:

df/dx = df/dg * dg/dx (notation of leibeniz)

so if you have y(t)=a * sin(x(t))) and you want to derive it from the time:

dy/dt = d(a*sin(x))/dx * dx/dt = a * cos(x) * dx/dt

this of course if at is constant both compared to t, and compared to x. if you then know the x trend over time, you can further specialize the dx/dt piece

by the way, it is called "derivata of a composed function"

 

[maxopus]

And you've got the coolest mind, and you've been able to explain it perfectly. Unfortunately, I haven't had a good analysis for more than 20 years, and it's time to take the books back. just for the taste to refresh my favorite matter.

 

[Wolverine]

Thanks for the answer! !

Hello! !