যেকোন গণিত সমস্যা সমাধান করুন

ধাপ ধাপে

1. f(x, y) = \sin{\left(x y \right)}

   The gradient is the vector of partial derivatives — differentiate with respect to each variable, holding the others constant.

2. \frac{\partial f}{\partial x} = y \cos{\left(x y \right)}

   Treat every variable except x as a constant.

3. \frac{\partial f}{\partial y} = x \cos{\left(x y \right)}

   Treat every variable except y as a constant.

4. \nabla f = \left[\begin{matrix}y \cos{\left(x y \right)}\\x \cos{\left(x y \right)}\end{matrix}\right]

   Assemble the gradient vector. It points in the direction of steepest ascent.

5. (0, 0)

   Critical points: where every partial derivative is zero.