Find the directional derivative of f(x,y,z) = xy^2 + x^2z + yz at the point P(1,1,2) in the direction of v = i + 2j - k.
Added by Laura C.
Step 1
The gradient of f is given by ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k. Calculate the partial derivatives: ∂f/∂x = y^2 + 2xz ∂f/∂y = 2xy + z ∂f/∂z = x^2 + y Evaluate these partial derivatives at the point P(1, 1, 2): ∂f/∂x = 1 + 4 = 5 ∂f/∂y = 2 + 2 = 4 ∂f/∂z = 1 + 1 = Show more…
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