Find df for f(x) = x² + 3x and evaluate it for
x = 2 and dx = 0.1

If U(x, y, z) = \(\frac { { x }^{ 2 }+{ y }^{ 2 } }{ xy } +3{ z }^{ 2 }y\), find \(\frac { \partial U }{ \partial x } ;\frac { \partial U }{ \partial y } \) and \(\frac { \partial U }{ \partial z } \)

If w(x, y, z) = x² y + y²z + z²x, x, y, z∈R, find the differential dw .

In each of the following cases, determine whether the following function is homogeneous or not. If it is so, find the degree.
\(U(x,y,z)=xy+sin\left( \frac { { y }^{ 2 }-2{ x }^{ 2 } }{ xy } \right) \)

Show that F(x,y) = \(\frac { { x }^{ 2 }+5xy-10{ y }^{ 2 } }{ 3x+7y } \) is a homogeneous function of degree 1.