Math Insight

Jacobian practice, 2 x 2 matrices

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  1. Calculate the Jacobian matrix of the function $\vc{ g }(x,y) = (10 x \ln{\left (x \right )},2 x \ln{\left (y \right )})$.


    $D\vc{ g }(x,y)=$




  2. Compute the Jacobian, $D\vc{f}$, of the multivariate function $\vc{f} (x,y)$ below, i.e. compute the matrix of partial derivatives. \[ \vc{f}(x,y) = (7 x^{2} + 4 x y + y^{2}, - 3 x - y ) \]



    $D\vc{f}=$




  3. Calculate the Jacobian matrix of the function $\vc{ f }(x,y) = (9 x^{3} e^{- 2 y},\left(x + 4\right) \log{\left (y + 1 \right )})$.


    $D\vc{ f }(x,y)=$




  4. Calculate the Jacobian matrix of the function $\vc{ h }(x,y) = (- 7 e^{3 x} - 3 e^{- y},- 2 e^{- 8 x + 7 y})$.


    $D\vc{ h }(x,y)=$