Derivative Of Power Series

Derivative power series is defined as the process performing differentiation operation for the given power series equation

. The power series is nothing but a polynomial equation whereas derivative of power series comes under calculus category. To find the rate of change for the given function calculus is broadly classified differential calculus and integral calculus. The following are the example problems with power series to find the derivatives.

Derivative of Power Series Example Problems:

Example 1:

Find the derivative for the given power series equation.

f(n) = n^4 3n 3 4n^2 + n

Solution:

The given function is

f(n) = n^4 3n 3 4 n^2 + n

The first derivative f ' for the algebraic function is

f '(n) = 4 n^3 3(3n^2) 4( 2 n ) + 1

f '(n) = 4 n^3 9n^2 8 n + 1

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Example 2:

Find the derivative for the given power series equation.

f(n) = n^5 6 n^3 + 11

Solution:

The given function is

f(n) = n^5 6 n^3 + 10

The first derivative f ' for the algebraic function is

f '(n) = 5n 4 6(3 n^2)

f '(n) = 5n 4 18 n 2

Example 3:

Find the derivative for the given power series equation.

f(n) = n^2 4n + 8

Solution:

The given equation is

f(n) = n^2 4n + 8

The first derivative f ' for the algebraic function is

f '(n) = 2 n 4

Example 4:

Find the derivative for the given power series equation.

f(n) = n^3 5 n^2 + 11n

Solution:

The given function is

f(n) = n^3 5 n^2 + 11n

The first derivative f ' for the algebraic function is

f '(n) = 3n^2 5(2 n ) + 11

f '(n) = 3n^2 10 n + 11

Derivative of Power Series Practice Problems:

1) Find the derivative for the given power series equation.

f(n) = n^2 6 n + 11

Answer: f '(n) = 2n 6

2) Find the derivative for the given power series equation.

f(n) = n^3 6 n^2 + 11n

Answer: f '(n) = 3n^2 12 n

by: johnharmer

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