Choose the expression that represents a cubic expression.
1 answer:
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ANSWER TO QUESTION 1
The given function is
The partial derivative of f with respect to x means we are treating y as a constant. The first derivative is
and the second derivative with respect to x is,
ANSWER TO QUESTION 2
The given function is
The partial derivative of f with respect to y means we are treating x as a constant. The first derivative is
and the second derivative with respect to y is
ANSWER TO QUESTION 3
Our first mixed partial is
We need to differentiate
again. But this time with respect to y.
Since this is a product of two functions of y, we apply the product rule of differentiation to obtain,
ANSWER TO QUESTION 4
The second mixed partial is
We need to differentiate
again. But this time with respect to x.
Since this is a product of two functions of x, we apply the product rule of differentiation to obtain,
Hence,
The given function is
The partial derivative of f with respect to x means we are treating y as a constant. The first derivative is
and the second derivative with respect to x is,
ANSWER TO QUESTION 2
The given function is
The partial derivative of f with respect to y means we are treating x as a constant. The first derivative is
and the second derivative with respect to y is
ANSWER TO QUESTION 3
Our first mixed partial is
We need to differentiate
again. But this time with respect to y.
Since this is a product of two functions of y, we apply the product rule of differentiation to obtain,
ANSWER TO QUESTION 4
The second mixed partial is
We need to differentiate
again. But this time with respect to x.
Since this is a product of two functions of x, we apply the product rule of differentiation to obtain,
Hence,