ringearV

2021-02-22

Find the first partial derivatives of the following functions.

$f(x,y)=e{x}^{2}y$

SabadisO

Skilled2021-02-24Added 108 answers

Step 1

Obtain the first partial derivative of f with respect to x as shown below:

$\frac{\partial f}{\partial x}=\frac{\partial}{\partial x}\left({e}^{{x}^{2}y}\right)$

$={e}^{{x}^{2}y}\cdot \frac{\partial}{\partial x}\left({x}^{2}y\right)$

$={e}^{{x}^{2}y}\cdot \left(2xy\right)$

$=2xy{e}^{{x}^{2}y}$

Step 2

Obtain the first partial derivative of f with respect to y as shown below:

$\frac{\partial f}{\partial y}=\frac{\partial}{\partial y}\left({e}^{{x}^{2}y}\right)$

$={e}^{{x}^{2}y}\cdot \frac{\partial}{\partial y}\left({x}^{2}y\right)$

$={e}^{{x}^{2}y}\cdot \left({x}^{2}\right)$

$={x}^{2}{e}^{{x}^{2}y}$

Obtain the first partial derivative of f with respect to x as shown below:

Step 2

Obtain the first partial derivative of f with respect to y as shown below:

Jeffrey Jordon

Expert2021-12-21Added 2605 answers

Answer is given below (on video)

Find the local maximum and minimum values and saddle points of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function

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