Quandaries and Queries


Name: mussawar
Who is asking: Student
Level of the question: Secondary

Question: hi
my question is d/dxdy/dx) = d2y/dx2. why it is not equal to d2y/d2x.

plz if you can explain these to clear my confustion.



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


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