Calculus derivative question

[dullard]

Can you give me a list of simple looking equations that are difficult or impossible to find the derivative analytically? This list is easy for integrals, but I'm having a hard time thinking of ones for derivatives. Thanks for any suggestions.

 

[BlueWeasel]

I swore never to speak of this thing you call Calculus once I finished Differential Equations.

 

[Peetoeng]

Google "not/non differentiable everywhere"

 

[amoeba]

derivatives are much easier than integrals.

That said, you can try hyperbolic cos, sine functions....

 

[scorp00]

I think that there are special equations with natural log (ln) in them that must be solved iteratively by trial and error. I can't remember a specific example though.

 

[Tiamat]

There are partial differential equations that end with a Convolution of Laplace transforms, or Error functions...

 

[DrPizza]

Originally posted by: amoeba
derivatives are much easier than integrals.

That said, you can try hyperbolic cos, sine functions....

Those are among the easiest to take the derivatives of, regardless of their form

How's This?
or better yet: This Weierstrass Function

 

[DrPizza]

Or, how about something really simple:

f(x) = x!

 

[dullard]

Thanks for the suggestions DrPizza. I'm trying to come up with a homework assignment to force the kids to numerically differentiate. They are doing Newton's method for finding the roots of a system of equations and I don't want them solving it analytically (as that misses the point of my last week's worth of lectures). The functions you gave are a bit too complex for a simple homework assignment. For example, if they need f(x)=x! and want to use x=1.5, then it is not worth the battle of what to do in that case. Same goes with infinite sums, too much effort on their part which doesn't pertain to the subject of numerical derivatives.

 

[eLiu]

Why not just force them to do it numerically...? Even if it's easier analytically, you can still require them to do it the hard way--"it'll be on the test."

 

[chuckywang]

Originally posted by: DrPizza
Or, how about something really simple:

f(x) = x!

Factorials are usually only defined for positive integers, but you can extend the definition of a factorial to real numbers by using Gamma Functions.

For example, (1/2)! = sqrt(pi), I believe.

 

[dullard]

Originally posted by: eLiu
Why not just force them to do it numerically...? Even if it's easier analytically, you can still require them to do it the hard way--"it'll be on the test."

You always get 5% of the students ignoring the rules you put on each homework. So I wanted to make those few students squirm for hours and then finally give up and do what was asked. I'm sick that way I guess.