Let be given and a point. Further, let be vectors in. All the derivatives in the below answer options are computed at. Without further knowledge about other than that given in each statement below, which of the answer options below is correct?

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Let<br><img src='https://www.fatskills.com/images2/GradExams/283E8FD1-0054-446A-9214-AF88BD1A2688.png' height='21' width='95'/> be given and<br><img src='https://www.fatskills.com/images2/GradExams/0F8FD137-D202-4388-B1F9-B2F22EA184DE.png' height='21' width='57'/> a point. Further, let<br><img src='https://www.fatskills.com/images2/GradExams/54660B7D-EF17-4A79-982C-23A941010B2B.png' height='19' width='32'/> be vectors in<br><img src='https://www.fatskills.com/images2/GradExams/F6F9B3A0-9214-4771-B5AF-BA3902706F06.png' height='17' width='21'/>. All the derivatives in the below answer options are computed at<br><img src='https://www.fatskills.com/images2/GradExams/18A8BC32-3908-48A9-9494-A2E82313B25F.png' height='13' width='11'/>. Without further knowledge about<br><img src='https://www.fatskills.com/images2/GradExams/E8929E27-9E39-4AB9-BA64-3CC4CD8D55B5.png' height='18' width='10'/> other than that given in each statement below, which of the answer options below is correct?