zepp Group Title derivative of an integral $\frac{d}{dx}\int f(x^2)dx^2$ one year ago one year ago

1. zepp Group Title

i've never seen a $$\large dx^2$$, anyone can explain to me what it is?

2. saifoo.khan Group Title

Zippy! Me meet again. ;D

3. zepp Group Title

ohai saif :D

4. saifoo.khan Group Title

not sure how to solve this. :/

5. AccessDenied Group Title

I recommend attempting the substitution: $$\sqrt{u} = x$$. Just a hunch that it may turn out well (and not because I just explained the solution on irc chats). I think it may be helpful to our problem so that the f(x^2) dx^2 becomes f(u) du, etc...

6. AccessDenied Group Title


7. tkhunny Group Title

Another Way: $$\de{x}\int f(x^{2})\;dx^{2} = \de{x}\int f(x^{2})\cdot 2x\;dx = \de{x} \left(F(x^{2}) + C\right) = f(x^{2})\cdot 2x$$ Same thing, really.