Question
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Let
(a) Evaluate at
(b) Evaluate at

Ask by Dawson Watkins. in Nigeria
Jan 11,2025

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Tutor-Verified Answer

Answer

Part (a):
At , the partial derivative is .
Part (b):
At , the partial derivative is .

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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:

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