Higher order derivatives (look for a pattern)

If a question asks you to find a higher-order derivative, then we should differentiate the function a few times and look for a pattern. Of course, you should remember all the derivative techniques such as the power rule, product rule, quotient rule, and chain rule.

0:00 Q1 higher-order derivative of ln(x)
5:23 Q2 higher-order derivative of cos(x)
9:17 Q3 higher-order derivative of sin(2x)
13:02 Q4 higher-order derivative of sqrt(e^x)
15:36 Q5 higher-order derivative of x*e^x

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"Just Calculus" is dedicated to helping students who are taking precalculus, AP calculus, GCSE, A-Level, year 12 maths, college calculus, or high school calculus. Topics include functions, limits, indeterminate forms, derivatives, and their applications, integration techniques and their applications, separable differential equations, and a lot more. Feel free to leave calculus questions in the comment section and subscribe for future videos.
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Best wishes to you,
Just calculus.

[ampisiades]

Thanks bprp for these free calc lessons.

The best way to spend my evenings.

[yoav]

Next challenge: find apattern(formula) for the integral (sinx)^n/x^n from 0 to inf

[sokolovrasputin]

big kobe fan? 8, 24, 81, 1996, and 2016 are all pretty coincidental

[lordstevenson]

Perfect timing, I just started higher order derivatives in my lectures

[Shreyas_Jaiswal]

Do you know I can define n! (n factorial) as d^n(x^n)/dx^n. In simple word, nth derivative of x^n.

[Magnus-]

I don't think I got the numbers right but I noticed a few things:

Question 1-4: The number (8, 24, 81 and 1996) is divisible by the question number. It just doesn't match with 2016 in question 5.

For the 81: I remember you did a video on 1/81 and it's "missing" 8's a long time ago. It could be in 2013 which is 8 years ago.

[yoav]

This reminds me number theory with the order mod n and primitive root. Number theory calculus the order of cosx is 4😀

[vitalsbat]

hi bprp, i wanna ask is there a f(x) with dn/dxn f(x) = (x+n)e^(x+n) ? please answer. thanks for the video!

[mathiasjeppesen]

I’ve found a pattern for the integral of ln^n(x) dx. The integral of ln^n(x) is equal to the sum from k = 0 to n of ((-1)^k * ln^(n-k) * n!/(n-k)!).. Tho I haven’t really proven why this is the case for all n. Can anyone help me with that?

[loandx]

Couldn't you also just say that dⁿ/dxⁿ(cos(x)) = cos(x+nπ/2) and dⁿ/dxⁿ(sin(2x)) = 2ⁿsin(x+nπ/2)

[yoav]

The last example is the easiest for achange!

[rabahazzoug]

How can we calculate the nth derivitive of f=e^(x^2)

[denischen]

What is the pattern for the nth derivative of tan(x)?

[NonTwinBrothers]

Wait so did he like prerecord a bunch of these then only now upload them?

[pneujai]

can we have a general chen lu for nth derivative

[pranavr]

7:40 Dividing what by what ? I don't get it

[neuralwarp]

It would be more satisfying if you did a proper proof by induction.

[shubhammygt]

I want to make a video in straight line.

[aydenherold]

My Teacher: Now, what is the 100th derivative of sec(x)?

[dqrksun]

find the 69th derivative of cosx+isinx with respect to i plspls