Partial Derivatives of Surface Equations and Clairaut's Theorem
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Find all the second partial derivatives.
47. f(x, y) = x^4 - 3(x^2)(y^3)
Verify that the conclusion of Clairaut's Theorem holds, that is, u_xy = u_yx.
55. u = ln[sqrt(x^2 + y^2)]
Find the indicated partial derivative.
59. f(x, y, z) = cos(4x + 3y + 2z); f_xyz, f_yzz
89. If f(x,y) = x(x^2 + y^2)^-3/2 * e^(sin(x^2 * y)), find (f_x)(1, 0). Hint: Instead of finding (f_x)(x,y) first, not that it's easier to use Equation 1 or Equation 2.
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Partial Derivatives of Surface Equations and Clairaut's Theorem are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
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