e1s2kat26

2021-05-30

Solve. partial derivatives of $\mathrm{\u25b3}=x{e}^{y}{10}^{ex}$

Tuthornt

Skilled2021-05-31Added 107 answers

Step 1

Consider the provided equation,

$\mathrm{\u25b3}=x{e}^{y}{10}^{ex}$

Find the partial derivatives of the above equation.

First, we find the derivative with respect to x.

$\frac{\partial \mathrm{\u25b3}}{\partial x}=\frac{\partial}{\partial x}(x{e}^{y}\cdot {10}^{ex})$

$={e}^{y}\frac{\partial}{\partial x}(x\cdot {10}^{ex})$

$={e}^{y}(\frac{\partial}{\partial x}\left(x\right){10}^{ex}+\frac{\partial}{\partial x}\left({10}^{ex}\right)x)$

$={e}^{y}({10}^{ex}+e\mathrm{ln}\left(10\right)\cdot {10}^{ex}x)$

Step 2

Now, we find the derivative with respect to y.

$\frac{\partial \mathrm{\u25b3}}{\partial y}=\frac{\partial}{\partial y}(x{e}^{y}\cdot {10}^{ex})$

$=x\cdot {10}^{ex}\frac{\partial}{\partial y}\left({e}^{y}\right)$

$=x\cdot {10}^{ex}{e}^{y}$

$={10}^{ex}x{e}^{y}$

Hence.

Consider the provided equation,

Find the partial derivatives of the above equation.

First, we find the derivative with respect to x.

Step 2

Now, we find the derivative with respect to y.

Hence.

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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