Question

Calculus question and work will follow. Need help on the conceptual part.

Answer 1

Is the quantity \[\frac{ ∂^2 f }{ ∂ x^2 }\] a scalar or a vector when \[f(x,y)=5ye^{7x^2y}\]?

I have found \[\frac{ ∂^2 f }{ ∂ x^2 }\] to be \[70y^2e^{7x^2y}+980x^2y^3e^{7x^2y}\]

Answer 2

f(x,y) is a function from R^2->R. So it is a scalar cuontity. It's derivative is also a scalar since it is just another function

Answer 3

Okay, thank you! So, the derivatives are also R^2 -> R ?

Answer 4

yes

Answer 5

Its a scalar. Derivative gives u instantaneous rate of change and second derivative gives u the same for the previous derivative function. For example, the second derivative of position function x(t) gives u the magnitude of its acceleration a(t)