List of top Engineering Mathematics Questions on Partial derivatives asked in GATE AG

If \( u = x^4 + y^4 + 3x^2 y^2 \), the value of \( \left( x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} \right)^{-1} \) is:

The slope of the function \( f(x) = 2x^4 - 3x^2 + 5x \) at \( x = 2 \) is _____. \(\textit{[Answer in integer.]}\)

Determinant of a matrix remains unaltered if __________.