Find the four second partial derivatives. Observe that the second mixed partials are equal. z=\ln(x-y)

Kaycee Roche

Kaycee Roche

Answered question

2021-05-03

Find the four second partial derivatives. Observe that the second mixed partials are equal.
z=ln(xy)

Answer & Explanation

FieniChoonin

FieniChoonin

Skilled2021-05-04Added 102 answers

Step 1
z=ln(xy)
dzdx=1xy
d2zdx2=1(xy)2...(1)
Step 2
dzdy=1xy
d2zdy=1xy
d2zdy2=1(xy)2(2)
From eq(1) and (2)
d2zdx2=d2zdy2
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-20Added 2605 answers

Answer is given below (on video)

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