Shirley Thompson

2021-12-30

Find all the second partial derivatives. $v=\frac{xy}{x-y}$

lovagwb

Beginner2021-12-31Added 50 answers

Partially differentiate with respect to x (use the quotient rule)

Partially differentiate with respect to y (use the quotient rule)

Partially differentiate

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ol3i4c5s4hr

Beginner2022-01-01Added 48 answers

Initial equation for 8e

$T={e}^{-2r}\mathrm{cos}\theta$

Find first partial derivative wrt. r

${T}_{r}=-2{e}^{-2r}\mathrm{cos}\theta$

Find second partial derivative wrt. r

${T}_{rr}=4{e}^{-2r}\mathrm{cos}\theta$

Find partial derivative wrt. theta

${T}_{\theta}=-{e}^{-2r}\mathrm{sin}\theta$

Find second partial derivative wrt theta

${T}_{\theta \theta}=-{e}^{-2r}\mathrm{cos}\theta$

Find the second partial derivative wrt the alternative variable

${T}_{r\theta}={T}_{\theta r}=2{e}^{-2r}\mathrm{sin}\theta$

Result:${T}_{rr}=4{e}^{-2r}\mathrm{cos}\theta ;\text{}{T}_{\theta \theta}={e}^{-2r}\mathrm{cos}\theta ;\text{}{T}_{r\theta}={T}_{\theta r}=2{e}^{-2r}\mathrm{sin}\theta$

Find first partial derivative wrt. r

Find second partial derivative wrt. r

Find partial derivative wrt. theta

Find second partial derivative wrt theta

Find the second partial derivative wrt the alternative variable

Result:

karton

Expert2022-01-08Added 613 answers

Find each first partial derivative, using the quotient rule.

Find each second partial derivative, using the quotient rule.

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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