Question

if u=log(xy) then du/dx is eual to​

Answer 1

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

$\mathsf{u=log\,(xy)}$

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

$\mathsf{\dfrac{\partial\,u}{\partial\,x}}$

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

$\mathsf{Consider,}$

$\mathsf{u=log\,(xy)}$

$\textsf{Using Product rule of logarithm, this can be written as}$

$\mathsf{u=log\,x+log\,y}$

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

$\mathsf{\dfrac{\partial\,u}{\partial\,x}=\dfrac{1}{x}+0}\;\;\;\;\;\mathsf{(\because\,keeping\;y\;as\;constant)}$

$\boxed{\bf\dfrac{\partial\,u}{\partial\,x}=\dfrac{1}{x}}$