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\(Let\quad X\quad =\quad \left( \begin{matrix} { x }^{ n } & \sin { x } & \cos { x } \\ n! & \sin { \frac { n\pi }{ 2 } } & \cos { \frac { n\pi }{ 2 } } \\ { a } & { a }^{ 2 } & { a }^{ 3 } \end{matrix} \right) \)

Then find \(\frac { { d }^{ n } }{ d{ x }^{ n } } (X)\) at \(x=0\)

Thanks guys, and please help me by posting complete solutions as i need to compare my solution. Thanks!!:)

Note by Abhineet Nayyar
2 years, 3 months ago

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Is its answer zero? @Abhineet Nayyar Tanishq Varshney · 2 years, 3 months ago

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@Tanishq Varshney @Tanishq Varshney , yea, but I need to confirm if my solution is legit or just some luck, Lol. Can you post your solution, please?? Abhineet Nayyar · 2 years, 3 months ago

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@Abhineet Nayyar i hope u know the technique of differentiating a matrix that is first differentiate first row leaving 2nd and 3rd row constant, added by differentiation of 2nd row leaving 1st and 3rd row added by differentiating 3rd row leaving 1st and 2nd Tanishq Varshney · 2 years, 3 months ago

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@Tanishq Varshney Yea, with that, i was able to evaluate this matrix into a single matrix, as the 2nd and 3rd row are constants and their derivatives will be zero. For the first element, i got the value of \(n!\) and for the second and third element of the first row, i tried to make cases, and got the answer 0. Abhineet Nayyar · 2 years, 3 months ago

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