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Math Help - Taking the partial derivative

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by tbyou87 View Post
    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:
    v(x, t) = u(z, t) where z = x + ct.

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

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

    -Dan
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  3. #3
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    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.
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