The "100-Followers" Note!!!

First of all, thanks to all my friends who took their time to follow me!!! Now,

$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!!:)

#Matrices

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Is its answer zero? @Abhineet Nayyar

Tanishq Varshney - 6 years, 2 months ago

@Tanishq Varshney , yea, but I need to confirm if my solution is legit or just some luck, Lol. Can you post your solution, please??

A Former Brilliant Member - 6 years, 2 months ago

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 - 6 years, 2 months ago

@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.

A Former Brilliant Member - 6 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$