Lesson 4

Partial Differentiation

Topics

  • All Topics
  • Partial Differentiation

    2 If $u=x^2-y^2 \; , \; v=2xy \; and \; z=f(u,v) $ prove the following

    $ (\dfrac{\partial z}{\partial x})^2 + (\dfrac{\partial z}{\partial y})^2 \;=\; 4\sqrt{u^2+v^2} \bigg[ (\dfrac{\partial z}{\partial u})^2 + (\dfrac{\partial z}{\partial v})^2 \bigg] \ \; \ \; \ \; \ $

    Read Full →
    6 If $ u \;=\; f \bigg( \dfrac{x-y}{xy} , \dfrac{z-x}{xz} \bigg) $ prove the following

    prove that

    $ x^2 \dfrac{\partial u}{\partial x} + y^2 \dfrac{\partial u}{\partial y} + z^2 \dfrac{\partial u}{\partial z} \;=\; 0 $

    Read Full →
    8 If $ \dfrac{x^2}{1+u}+\dfrac{y^2}{2+u}+\dfrac{z^2}{3+u}=1 $ then prove the following

    Prove : $ \bigg(\dfrac{\partial u}{\partial x} \bigg)^2 + \bigg(\dfrac{\partial u}{\partial y} \bigg)^2 + \bigg(\dfrac{\partial u}{\partial z} \bigg)^2 \;=\; 2 \bigg( x\dfrac{\partial u}{\partial x} + y\dfrac{\partial u}{\partial y} + z \dfrac{\partial u}{\partial z} \bigg) \\ \; \\ $

    Read Full →