Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

is there a difference between $\frac{\partial^2 }{\partial x^2}$ and $(\frac{\partial }{\partial x})^{2}$? I have to tell if a differential equation is linear, and $(\frac{\partial }{\partial x})^{2}$ concerns me. If it's the same thing as second derivative, the equation would be linear.

share|cite|improve this question
Same thing; it means the operator $\partial / \partial x$ applied twice. – anon Apr 1 '12 at 20:27
Is the notation $\frac{\partial^2}{\partial x^2}$ also used in the same text? If so, that would seem to indicate that the author intends for $(\frac{\partial}{\partial x})^2$ to mean something different, in which case Tom Au's answer below seems to be correct. – Santiago Canez Jan 30 '14 at 23:00
up vote 2 down vote accepted

the notation $\frac{\partial^2 }{\partial x^2}f~~$ means $\frac{\partial }{\partial x}(\frac{\partial }{\partial x}f)$, so $\frac{\partial^2 }{\partial x^2}f~~$ and $(\frac{\partial }{\partial x})^{2}f~~$ is the same both you apply $\frac{\partial }{\partial x}$ twice.

share|cite|improve this answer

The first expression, $\frac{\partial^2 }{\partial x^2}$ is the second (partial) derivative, while the second expression, $(\frac{\partial }{\partial x})^{2}$, is the first (partial) derivative squared.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.