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Section 13.5 : Differentials

2. Compute the differential of the following function.

\[f\left( {x,y,z} \right) = \ln \left( {\frac{{x{y^2}}}{{{z^3}}}} \right)\] Show Solution

Not much to do here. Just recall that the differential in this case is,

\[df = {f_x}\,dx + {f_y}\,dy + {f_z}\,dz\]

The differential is then,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{df = \frac{1}{x}dx + \frac{2}{y}\,dy - \frac{3}{z}dz}}\]