Question

Find the second partial derivative of z = x3 + y3
– 3axy.

Answer 1

Answer:

Therefore, the second partial derivative of z = x³ + y³ – 3axy with respect to x and y is -3a.

Step-by-step explanation:

To find the second partial derivative of z = x³ + y³ – 3axy, we need to differentiate the function twice, once with respect to x and then with respect to y.

Let's start with the first partial derivative with respect to x:

∂z/∂x = 3x² – 3ay

Now, we can take the partial derivative of this expression with respect to y to find the second partial derivative of z with respect to x and y:

∂²z/∂y∂x = ∂/∂y (3x² – 3ay)

= -3a

Now, we can take the partial derivative of the original function with respect to y to find the first partial derivative with respect to y:

∂z/∂y = 3y² – 3ax

Finally, we can take the partial derivative of this expression with respect to x to find the second partial derivative of z with respect to y and x:

∂²z/∂x∂y = ∂/∂x (3y² – 3ax)

= -3a

Therefore, the second partial derivative of z = x³ + y³ – 3axy with respect to x and y is -3a.

To know more about the second partial derivative refer:

https://brainly.in/question/28270073

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