Which of the following substitutions produces the triple product rule (with all uppercase symbols): (?w/?x)_X (?y/?Y)_Z (?Z/?X)_z=-1
A. w = W, x = Y, y = Z, z = Y
B. w = X, x = Y, y = Z, z = Y
C. w = Z, x = Y, y = X, z = Y
D. w = Y, x = Z, y = X, z = Y
E. Multiple possibilities/Too many degrees of freedom
A. Incorrect. W is used as a fourth variable and there is no fourth variable in the triple product rule.
B. Incorrect. This results in the first derivative being the change in X at constant X, which is zero. This collapses the entire equation into 0 = -1; a clear inequality.
C. Incorrect. This results in two partial derivatives with varying Y. In the triple product rule, each variable (X, Y, and Z) only occupies a certain position once in the three derivatives.
D. Correct. Making these substitutions, the triple product rule is recovered.
E. Incorrect. There is only one set of equalities possible that will satisfy the equation. Leave the first one (constant X) for last.
?
You might also like to view...
A systematic approach known as the_________ has been generally adopted as the standard procedure for conducting research
Fill in the blank(s) with correct word
It is projected that global warming will lead to a net loss of cropland
Indicate whether the statement is true or false
Animal waste can be used on organic crops if it is properly composted first
Indicate whether the statement is true or false
When should DTCs be cleared?
A) After the problem has been verified. B) After the repair has been verified. C) After pinpointing a problem cylinder D) After consulting TSBs