Quiz 5

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Total points: 8

Compute the derivative, $\frac{dg }{dy }$, of the function $g(y)$ below \[ g(y) = y^{3} e^{5 y}. \]
$g'(y) = $
Let $g(x,y) = - 4 x^{2} + 2 x y^{2} + 2 x y$. Calculate the partial derivatives of $g$.

$\displaystyle \pdiff{ g }{ x } = $

$\displaystyle \pdiff{ g }{ y } = $
Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = \ln{\left (6 x^{2} + 3 x + 4 \right )}. \]
$f'(x) = $
Compute the Jacobian, $D\vc{f}$, of the multivariate function $\vc{f} (x,y)$ below, i.e. compute the matrix of partial derivatives. \[ \vc{f}(x,y) = (10 x^{2} + 4 x y - 4 y^{2}, 4 x ) \]

$D\vc{f}=$
Given the function \[ f( z ) = \left(z^{3} - 3 z\right) e^{z}, \] calculate the slope of the tangent line at the point $z=-4$.

tangent line slope =

Do not round or approximate your answer.