Q32-33 p711

In Exercises 32-33, find fx, fy, fz, fyz and fzy.

\(f(x, y,z) = x^3y^2 + x^3z + y^2z\)

\(fx = x^3y^2 + x^3z + y^2z dx\)
\(fx = 3x^2y^2 + 3x^2z\)

\(fy = x^3y^2 + x^3z + y^2z dy\)
\(fy = 2x^3y + 2yz\)

\(fz = x^3y^2 + x^3z + y^2z dz\)
\(fz = x^3 + y^2\)

\(fyz = 2x^3y + 2yz dz\)
\(fyz = 2y\)

\(fzy = x^3 + y^2 dy\)
\(fzy = 2y\)

\(f(x, y,z) = \frac{3x}{7y^2z}\)

\(fx = \frac{3x}{7y^2z} dx\)
\(fx = \frac{3}{7y^2z}\)

\(fy = \frac{3x}{7y^2z} dy\)
\(fy = -\frac{6x}{7y^3z}\)

\(fz =\frac{3x}{7y^2z} dz\)
\(fz = -\frac{3x}{7y^2z^2}\)

\(fyz = -\frac{6x}{7y^3z} dz\)
\(fyz = \frac{6x}{7y^3z^2}\)

\(fzy = -\frac{3x}{7y^2z^2} dy\)
\(fzy = \frac{6x}{7y^3z^2}\)