Take the 2-minute tour ×
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.

Assuming that $u = f(x,y)$, $x = e^s\sin(t)$, $y = e^s\sin(t)$

Show that $(\frac{\partial u}{\partial s})^2 \neq \frac{\partial^2 u}{\partial d s^2}$

I know what to do, but I don't know how to do it. The RHS gives me difficulties.

share|improve this question
    
Were $x$ and $y$ intended to be the same? Is $\sin$ a part of the exponent? How is this discrete? –  Karolis Juodelė Nov 14 '12 at 17:01
    
doesn't discrete math involve proofs? –  Arnold Nov 14 '12 at 17:02
    
All math involves proofs. Discrete is the opposite of continuous. Discrete math involves things like number theory, graphs, etc. –  Karolis Juodelė Nov 14 '12 at 17:04
    
Are you sure is $\frac{\partial^2 u}{\partial ds^s}$ is well written? It doesn't have meaning at all. Also, related: math.stackexchange.com/q/235103/19532 –  Pragabhava Nov 14 '12 at 18:04

1 Answer 1

Since $x=y$, let $f(x,y)=g(x)\\ \frac{\mathrm{d}u}{\mathrm{d}s}=x\frac{\mathrm{d}g}{\mathrm{d}s}\\ \frac{\mathrm{d}^2u}{\mathrm{d}s^2}=\frac{\mathrm{d}g}{\mathrm{d}s}+x\frac{\mathrm{d}^2g}{\mathrm{d}s^2}$

Setting $h=\frac{\mathrm{d}g}{\mathrm{d}s} \ \, \ \frac{\mathrm{d}u}{\mathrm{d}s}=\frac{\mathrm{d}^2u}{\mathrm{d}s^2} \text{iff} \frac{\mathrm{d}h}{\mathrm{d}s}=xh^2-\frac{h}x$. Since a solution must exist, they are unequal only for almost all $u$.

share|improve this answer

Your Answer

 
discard

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.