Question

Find ∇f and its value at P:

a) f = eˣ cos y, P: (1, π/2)
b) f = cos x cosh y, P: (π/2, ln 2)

Answer 1

To find ∇f and its value at P, we need to find the partial derivatives of f with respect to each variable and evaluate them at point P.

Step-by-step explanation:

To find ∇f and its value at P, we need to find the partial derivatives of f with respect to each variable and evaluate them at point P.

a) For f = eˣ cos y, the partial derivatives are ∂f/∂x = eˣ cos y and ∂f/∂y = -eˣ sin y. Evaluating these at P(1, π/2) gives ∂f/∂x = e and ∂f/∂y = -e.

b) For f = cos x cosh y, the partial derivatives are ∂f/∂x = -sin x cosh y and ∂f/∂y = cos x sinh y. Evaluating these at P(π/2, ln 2) gives ∂f/∂x = 0 and ∂f/∂y = 2.