Question

If a displacement field is given by u = x² + 2y², what is the displacement in the x-direction?

1) 2x
2) 2y
3) 2xy
4) 2x²

Answer 1

The displacement in the x-direction is 2x.

Step-by-step explanation:

The displacement in the x-direction can be found by taking the partial derivative of the displacement field u = x² + 2y² with respect to x. This derivative will give us the rate of change of u with respect to x. Applying the power rule of derivatives, we can differentiate x² to get 2x. Therefore, the displacement in the x-direction is 2x, which corresponds to option 1.