If dy/dx=2xy, then d2y/dx2=

Question

idku · Answer

$\displaystyle\frac{dy}{dx}=2xy$

idku · Answer

Can you do the product rule on this?

bmk614 · Answer

Yes. I did that and got $$2y+2x \frac{ dy }{ dx }$$

bmk614 · Answer

and then I plugged that in

idku · Answer

Differentiate both sides like you normally would ...
Product side for the left side (with a chain rule of y' (or dy/dx) for every derivative of y), and the right side, when differentiate, is just a second derivative.

Note that your second derivative is in terms of the first derivative, but you already know that your first derivative is y'=2xy, so plug that in as well.

idku · Answer

Product rule, not product side , sorry.

bmk614 · Answer

$$2y+4x^2y$$

phi · Answer

yes

idku · Answer

$\displaystyle\frac{dy}{dx}=2xy$

$\displaystyle\frac{d^2y}{dx^2}=2y+2x\frac{dy}{dx}$

$\displaystyle\frac{d^2y}{dx^2}=2y+2x(2xy)=?$

bmk614 · Answer

But the answer is$$4x^2y$$

idku · Answer

No it is not, unless the problem is different.

bmk614 · Answer

No that is the problem. But I looked at the answer key and that was the answer.

idku · Answer

well, your answer key is wrong then

bmk614 · Answer

So the company that made the book and the answer key are wrong?

idku · Answer

all I can say is that 4x^2y is for sure not the answer.
The answer is definitely, 2y+2x^2y.

bmk614 · Answer

well that is what I thought too, but apparently not.

idku · Answer

Ask your teacher...

idku · Answer

and again the answer key is for sure wrong.

idku · Answer

You can ask literally anyone who knows math online, offline, in hell or in paradise.

idku · Answer

Again,

$\displaystyle \frac{dy}{dx}=2xy$

$\displaystyle \frac{d^2y}{dx^2}=2y+2x\frac{dy}{dx}=2x+2y(2xy)=2x+4x^2y.$


Good luck!

bmk614 · Answer

Chill, I agree with you.

idku · Answer

ok