Question

2 find the second order partial derivatives of e^x-y​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{e^{x-y}}$

$\underline{\textbf{To find:}}$

$\mathsf{Second\;order\;partial\;derivaties\;of\;e^{x-y}}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\;z=e^{x-y}}$

$\textsf{Differentiate partially with respect to 'x'}$

$\mathsf{\dfrac{\partial\,z}{\partial\,x}=e^{x-y}}$

$\textsf{Differentiate again partially with respect to 'x'}$

$\implies\boxed{\mathsf{\dfrac{\partial^2\,z}{\partial\,x^2}=e^{x-y}}}$

$\mathsf{z=e^{x-y}}$

$\textsf{Differentiate partially with respect to 'y'}$

$\mathsf{\dfrac{\partial\,z}{\partial\,y}=e^{x-y}(-1)=-e^{x-y}}$

$\textsf{Differentiate again partially with respect to 'y'}$

$\mathsf{\dfrac{\partial^2\,z}{\partial\,y^2}=-e^{x-y}(-1)}$

$\implies\boxed{\mathsf{\dfrac{\partial^2\,z}{\partial\,y^2}=e^{x-y}}}$

$\underline{\textbf{Find more:}}$

Find the second order partial derivatives of F(x.y) = (3x + 2y).4​

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