Problem 1.45. As an illustration of why it matters which variables you hold fixec when taking partial derivatives, consider the following mathematical example. Le w = zy and z = yz. (a) Write w purely in terms of z and z, and then purely in terms of y and z. (b) Compute the partial derivatives and and show that they are not equal. (Hint: To compute (ðw/ðz)y, use i formula for w in terms of z and y, not z. Similarly, compute (ðu/ðr): from a formula for w in terms of only z and z.)
Problem 1.45. As an illustration of why it matters which variables you hold fixec when taking partial derivatives, consider the following mathematical example. Le w = zy and z = yz. (a) Write w purely in terms of z and z, and then purely in terms of y and z. (b) Compute the partial derivatives and and show that they are not equal. (Hint: To compute (ðw/ðz)y, use i formula for w in terms of z and y, not z. Similarly, compute (ðu/ðr): from a formula for w in terms of only z and z.)
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Transcribed Image Text:Problem 1.45. As an illustration of why it matters which variables you hold fixec
when taking partial derivatives, consider the following mathematical example. Le
w = ry and z = yz.
(a) Write w purely in terms of x and z, and then purely in terms of y and z.
(b) Compute the partial derivatives
and
and show that they are not equal. (Hint: To compute (ðu/dz)y, use i
formula for w in terms of r and y, not z. Similarly, compute (ðu/ar}:
from a formula for w in terms of only z and z.)
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