Name: mussawar
Who is asking: Student
Level of the question: Secondary
Question: hi
my question is d/dx( dy/dx) = d2y/dx2. why it is not equal to d2y/d2x.
plz if you can explain these to clear my confustion.
thanks
Hi Mussawar,
Think of d/dx as an operator. It operates on a function and gives you the derivative of the function. So
d/dx(x3 + x) = x2 + 1
If you now want the second derivative you differentiate again and get
d/dx [ d/dx(x3 + x)] = d/dx [ x2 + 1] = 2x
Using this notation, if the function you want to differentiate is y then the derivative is
d/dx(y)
and the second derivative is
d/dx [ d/dx(y) ]
Now I can treat this as an operator that operates on a function and gives you the second derivative. What I see is
d/dx ( d/dx) (y)
so the operator that says "second derivative" is
d/dx ( d/dx)
To simplify the notation we sometimes write this as
d/dx ( d/dx) = d2/(dx)2 or to simplify even more d2/dx2
Penny
