Higher-order derivatives, Mathematics

Assignment Help:

Higher-Order Derivatives

It can be seen that the derivative of a function is also a function.

Considering f'x as a function of x, we can take the derivative of  f'x which will yield another function, say f''x. This is called the second derivative of f(x). The third derivative of f(x) is the derivative of the second derivative f''x. We can take derivatives of higher orders by repeating the process. The second, third, fourth, (etc.) derivatives are symbolically written as:

1638_higher order derivative.png 

Example 

Let     f(x)

=

  3x3 + 2x2 - 4x + 6

f'x

=

 9x2 + 4x - 4

f''x

18x + 4

f''x

=

18
f(4) (x)

=

0
f(5) (x)

=

 0

"

   

"

   

"

   
f(n) (x)

=

0

Related Discussions:- Higher-order derivatives

Show that 571 is a prime number, Show that 571 is a prime number. Ans: ...

Show that 571 is a prime number. Ans:    Let x=571⇒√x=√571 Now 571 lies between the perfect squares of  (23)2 and (24)2 Prime numbers less than 24 are 2,3,5,7,11,13,17,1

Determinarte, what is the differeance in between determinate and matrix .

what is the differeance in between determinate and matrix .

Volume of grains in the silo , The volume of grains in a silo at a particul...

The volume of grains in a silo at a particular time (measured in hours) is given by V (t) = 4t(3-t) m3. Find the rate of change of the volume of grains in the silo from first princ

Simple random sampling, Simple Random Sampling It refers to the samplin...

Simple Random Sampling It refers to the sampling technique whether each and every item of the population is described an equal chance of being included in the sample. Because s

Alcohol solution (mixture), Nora works at a laboratory as a chemist . she w...

Nora works at a laboratory as a chemist . she was told to prepare 100L of 25% alcohol solution. she has on hand of a 15% percent alcohol solution and a 40% alcohol solution which s

Evaluate the infinite limits of given limits, Evaluate following limits. ...

Evaluate following limits. Solution Therefore we will taking a look at a couple of one-sided limits in addition to the normal limit here. In all three cases notice

Proof for absolute convergence - sequences and series, Proof for Absolute C...

Proof for Absolute Convergence Very first notice that |a n | is either a n or it is - a n depending upon its sign.  The meaning of this is that we can then say, 0 a n +

What is the meaning of the f-statistic and f test, You are given the follow...

You are given the following regression results estimating the demand for widgets based on time series data for the past 40 months. Q t = 2.5 - 0.3 x P t + 12 x M t Where Q

Subtraction involving negative numbers, Q. Subtraction Involving Negative N...

Q. Subtraction Involving Negative Numbers? In order to subtract positive and negative numbers, you need to be aware of the Rule for Subtraction. This rule states that subtracti

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd