first and second order partial derivative easy questions

It has been a long time since I've had to do derivatives so I'm rusty.

show that where 'k' is constant.

I get :

and

so if I multiply the second order derivative (U_xx) by 'k' then this should be correct?

I just want to make sure that since I'm doing partial derivatives with respect to x for the last 2 that I can ignore the because it is all a cosntant. And when I do the derivative of I only need to pull the 'n' out and change it to cos(nx). Also, for the first derivative with respect to 't' I am taking the '1' exponent off of 't' and bringing it forward.

Last semester was 100% integrals and I feel like I have to relearn the first semester all over. Thanks for the help.

Also, just notices that my doesnt work. Anyone able to tell me how to get two sub x's in a row. Figured parathese would work, guess not.

Re: first and second order partial derivative easy questions

Re: first and second order partial derivative easy questions

You use braces: U_{xx} to give . To get the other notation, do \frac{\partial^2U}{\partial{x}^2} for . The braces around x in the denominator are just to separate it from the word "partial". A space works, too: \frac{\partial^2U}{\partial x^2} gives the same thing.

When you take the partial derivative with respect to x, t is held constant, so is a constant and you're just differentiating the sine function. The second derivative works the same way. So you go from sine to cosine to negative sine, and two factors of n come out.

When you take the partial derivative with respect to t, x is held constant, so is a constant any you're just differentiating the exponential, and a factor of comes out. So you have the same thing as with an additional factor of k.

When I take the derivative of , my thinking is that I bring down the coefficient of whatever I'm differentiating with respect to. Technically, I'm using the chain rule, so I'm multiplying by the derivative of ax.

- Hollywood