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Let f(x, y, z) = x + ln(2y + 3z 2 ). Compute ∂f ∂x, ∂ 2f ∂y∂x, and ∂ 3f ∂z∂y∂x. Evaluate ∂ 2f ∂y∂x(2, 1, −2).

Respuesta :

Answer:

Step-by-step explanation:

Given that

[tex]f(x, y, z) = x + ln(2y + 3z^2 )[/tex]

Let us find partial derivatives one by one

[tex]\frac{∂f }{∂x} =1\\\frac{∂^2f }{∂y∂x} =\frac{∂ }{∂y}(1) =0\\\frac{∂^3f }{∂z∂y∂x} =\frac{∂ }{∂z}(0) =0[/tex]

At the point (2,1,-2)

[tex]\frac{∂^2f }{∂y∂x}=0[/tex]

(since at all points the value is constant 0)

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