Question

what is the nth differential coefficient of x^n ​

Answer 1

SOLUTION

TO DETERMINE

The nth differential coefficient of $\sf{ {x}^{n} }$

EVALUATION

$\sf{Let \: \: y= {x}^{n} }$

Differentiating both sides with respect to x we get

$\sf{y_1 = n. {x}^{n - 1} }$

Again Differentiating both sides with respect to x we get

$\sf{y_2 = n. (n - 1){x}^{n - 2} }$

Performing the same differentiation upto n times we get

$\sf{y_n= n. (n - 1).(n - 2)...1 .{x}^{n - n} }$

$\sf{ \implies \: y_n= n. (n - 1).(n - 2)...1 .{x}^{0} }$

$\sf{ \implies \: y_n= n. (n - 1).(n - 2)...1 }$

$\sf{ \implies \: y_n= n!}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Find the slope of the chord of parabola y^2=4x whose midpoint is (1,1). Help with explanation

https://brainly.in/question/13409021

2. The length of the latus rectum of the parabola

13[(x-3)^2+(y-4)^2 )= (2x-3y+ 5)^2 is

https://brainly.in/question/24980361

3. A hyperbola has its center at (3, 4), a vertex at the point (9, 4), and the length of its latus rectum is 3 units. An ex...

https://brainly.in/question/30210645