Question

If \(z = 3x^2 y - x\sin(xy)\), then

• A. \(\frac{\partial^2 z}{\partial y \partial x} > \frac{\partial^2 z}{\partial x \partial y}\)
• B. \(\frac{\partial^2 z}{\partial y \partial x} < \frac{\partial^2 z}{\partial x \partial y}\)
• C. \(\frac{\partial^2 z}{\partial y \partial x} = \frac{\partial^2 z}{\partial x \partial y}\)
• D. \(\frac{\partial^2 z}{\partial y \partial x} = 0\)

Hint:

Always check if the function is continuous and has continuous partial derivatives.
Clairaut's theorem simplifies many problems.

Answer 1

The Correct Option is C