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Answer
Part (a):
At , the partial derivative
is
.
At
Part (b):
At , the partial derivative
is
.
At
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The Deep Dive
To find
, we will compute the partial derivatives and then evaluate them at the specified points.
(a) To find
, we use the product and chain rules.
Calculating the first term:
Calculating the second term using the chain rule:
So, the second term becomes:
Combining both parts, we have:
Now, evaluating at the point
:
Thus, the final answer for part (a) is:
(b) To find
(denoted
), we apply the chain rule:
Thus,
Now, evaluating at the point
:
Therefore, the final answer for part (b) is: