Is the following statement "If ( f(x, y, z)=x^{2} y^{3}-4 x z ) then the directional derivative of ( f ) in the direction ( vec{v}=langle-1,2,0 angle ) is [ D_{vec{u}} f=frac{1}{sqrt{5}}left(4 z+2 x y^{3}+6 x^{2} y^{2} ight) ] true or false? Select one: True False
Added by Saadet Burcu T.
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The gradient is given by the vector of partial derivatives: ∇f = ⟨∂f/∂x, ∂f/∂y, ∂f/∂z⟩ Now, let's find the partial derivatives: ∂f/∂x = 2xy^3 - 4z ∂f/∂y = 3x^2y^2 ∂f/∂z = -4x So, the gradient of f is: ∇f = ⟨2xy^3 - 4z, 3x^2y^2, -4x⟩ Show more…
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