Question

I know it's stupid but Someone please explain this to me.. Here x = f(t) then how is dx written as it is in image below?

Answer 1

if y =f (x)
then differentiation w.r.t. x
dy/dx =d (f (x))/dx
we also write df (x)/dx=f'(x) or , f1 (x)
now ,
given x=f (t)
differentiate w. r.t t
dx/dt =d (f (t)/dt =f'(t)

dx/dt =f'(t) ----------------(1)

dx=f'(t). dt
from equation (1)
dx=(dx/dt).dt