"Find the four second partial derivatives of the..." was answered by our community

Kyran Hudson

Answered question

2021-03-23

Find the four second partial derivatives of the following functions.

Q (r, s) = \frac{e^{r^{e} s}}{s}

Answer & Explanation

lamusesamuset

Skilled2021-03-25Added 93 answers

Step 1
Partial differential :

Q (r, s) = \frac{e^{r^{e} s}}{s}

\frac{\partial Q}{\partial r} = \frac{e r^{2} s e^{r^{3} s}}{s}

= 3 e^{r^{3} s} r^{2}

\frac{\partial Q}{\partial r} = \frac{s . r^{3} e^{r^{3} s} - e^{r^{3} s}}{s^{2}}

Step 2

\frac{\partial^{2} Q}{\partial r^{2}} = 3 (3 e^{r^{3} s} r^{4} s + 2 e^{r^{3} s} r)

\frac{\partial^{2} Q}{\partial s^{2}} = \frac{e^{r^{3} s} (r^{6} - s^{2} - 2 (r^{3} s - 1))}{s^{3}}

\frac{\partial^{2} Q}{\partial r \partial s} = 3 e^{r^{3} s} r^{5} = \frac{\partial^{2} Q}{\partial s \partial r}

Here are the four second partial derivatives of the function.

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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