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djeljenike

Answered question

2021-05-19

Find the four second partial derivatives of the following functions.

F (r, s) = r e^{s}

Answer & Explanation

au4gsf

Skilled2021-05-21Added 95 answers

Given,

F (r, s) = r e^{s}

Partially differentiating with respect to r, we get

F_{r} = e^{s} \cdot 1

= e^{s}

Partially differentiating with respect to s, we get

F_{s} = r e^{s}

Step 2
Now,

F_{r r} = \frac{\partial (F_{r})}{\partial r}

= \frac{\partial (e^{s})}{\partial r}

=0

F_{r s} = \frac{\partial (F_{r})}{\partial s}

= \frac{\partial (e^{s})}{\partial s}

= e^{s}

F_{r s} = \frac{\partial (F_{s})}{\partial r}

= \frac{\partial (r e^{s})}{\partial r}

= e^{s}

F_{s s} = \frac{\partial (F_{s})}{\partial s}

= \frac{\partial (r e^{s})}{\partial s}

= r e^{s}

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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