Compute the total differential of f(x, y, z) = 3 + x⁴yz². A) 4x³yz²dx dy dz B) 4x³yz²dx + x⁴yz²dy + 2x⁴yz²dz C) 4x³yz dx + x⁴yz²dy + x⁴yz²dz D) 4x³yz²dx + x⁴z²dy + 2x⁴yz dz E) 4xyzdx + xzdy + 2xyz dz

Question

Quizplus · Accepted Answer

The total differential of f(x, y, z) is found by taking the partial derivatives with respect to each variable and multiplying by the differential of that variable. The partial derivatives are: ∂f/∂x = 4x^3yz^2, ∂f/∂y = x^4z^2, ∂f/∂z = 2x^4yz. Thus, the total differential is 4x^3yz^2dx + x^4z^2dy + 2x^4yz dz.

Compute the Total Differential of F(x, Y, Z) = 3