Answer to Question #254020 in Calculus for Shabo

Question

n each part, compute à °  ‘ “

à ¢ € ²

, à °  ‘ “

à ¢ € ²Ãƒ ¢ € ²

, à °  ‘ “

à ¢ € ²Ãƒ ¢ € ²Ãƒ ¢ € ² and then state the formula for nth derivative à °  ‘ “

(à °  ‘ ›)

(a) à °  ‘ “(à °  ‘ ¥) = à °  ‘ ’

2à °  ‘ ¥

(b) à °  ‘ “(à °  ‘ ¥) = à °  ‘ à °  ‘ –à °  ‘ ›3à °  ‘ ¥

(c) à °  ‘ “(à °  ‘ ¥) = à °  ‘ ™Ãƒ °  ‘ ›Ãƒ °  ‘ ¥

Draw the graph of first three derivatives of à °  ‘ “(à °  ‘ ¥).

Answer 1

As the question is not clear ,

So providing basic idea to solve these types of questions.

Let,

Given: $\overrightarrow{A}=x^4 \overrightarrow{i}$

a) first derivative of $\overrightarrow{A}$

${ d\overrightarrow{A}\over dx}=4x^3 \overrightarrow{i}$

Graph:

b) second derivative of $\overrightarrow{A}$

${ d^2\overrightarrow{A}\over dx^2}=12x^2 \overrightarrow{i}$

c) third derivative of $\overrightarrow{A}$

${ d^3\overrightarrow{A}\over dx^3}=24x \overrightarrow{i}$

The formula for mth derivation of general term with nth exponential power is...

${dy^m\over dx^m}=n(n-1)..(n-m)x^{n-m}$

.