# Thread: Taking the partial derivative

1. ## Taking the partial derivative

Hi,

Let v(x,t) = u(x+ct,t).

Find partial of v with respect to x, second partial of v with respect to x and the partial with respect to t.

I'm just confused with the t's acting as x+ct and t by it self.

Thanks

2. Originally Posted by tbyou87
Hi,

Let v(x,t) = u(x+ct,t).

Find partial of v with respect to x, second partial of v with respect to x and the partial with respect to t.

I'm just confused with the t's acting as x+ct and t by it self.

Thanks
It's all about the chain rule. Think of your function u this way:
$\displaystyle v(x, t) = u(z, t)$ where $\displaystyle z = x + ct$.

So
$\displaystyle v_x = u_z \cdot \frac{\partial z}{\partial x} = u_z$
Then replace z with x + ct.

$\displaystyle v_t = u_z \cdot \frac{\partial z}{\partial t} + u_t$

-Dan

3. How would I substitute those values into the equation:

partial u with respect to t - k*second partial u with respect to x + C*partial u with respect to x = 0. Here k and C are constants.