# Items tagged with derivativederivative Tagged Items Feed

### Derivative of functions with constants...

November 18 2015
1 2

Hi everyone. Please excuse me in advance, as I am new on this website and to Maple.

So I am using Maple 16 and I want it to give me the derivative of a function that has constants in it, for example f(x)=(x-a)(x-b). I wrote the (probably stupid) commands on Maple:

> f(x):=(x-a)(x-b);

> diff(f(x), x);

but the result is not the expected (2x-a-b), but rather (D(x))(x-b)-(D(a))(x-b). What would be the right things to write to get what I need?

David

### IBS incorrect. How to write?...

October 15 2015
0 8

There is a desire to explore the process of filtration combustion. To do this, you must solve a system of differential equations in partial derivatives.
I write down all the equations.
Boundary conditions in Maple 2015.0 interpreted incorrectly.
I need to write like that:

given that:

It turns out so:

ie somewhere lost derivatives

,....

As in Maple record boundary conditions correct?

October 11 2015
0 3

Hi, I am trying to find adomian's polynomial of exp(y), but after execution it shows DF(e^y), D^2F(e^y) as it is. why it does'nt show its derivative?plz help meNewADP.2.mw

### Partial derivative syntax ...

September 28 2015
0 10

I am entering into Maple, but it interprets it as

How do I change this partial derivative to a total one. (Both x and y can be assumed invertible functions of parameter u and their derivatives are nonzero)

### Error in pdsolve...

September 06 2015
0 8

Hi everyone.

I have been experiencing a problem trying to solve a coupled system of 3 differencial equations

My problem is that a got a message back as I try to solve the system:

"Error, (in pdsolve/numeric/process_IBCs) improper op or subscript selector"

by apply this point that ''all dependent variables must be functions of the same independent variables''

i again accost with another error ''

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions can only contain derivatives which are normal to the boundary, got (D[1, 1](w))(x, -3/400000000)

''

### Programming and differentiation...

September 02 2015
3 2

I have an expression of derrivative, lets say (D[2, 2](G))(x, y).

How to get this numbers - [2,2] programmicaly from it?

### Second derivative of an ODE solution...

August 18 2015
3 9

Hi,
I'm new at maple and have a problem/question with the rkf45 numerical ODE Solver.

At first, my computer need a lot of time to calculate an analytic solution.
Therefor, I use the numerical way.

I have the following second order ODE:
ODE:=m*((D@@2)(x))(t)+d*(D(x))(t)+k*x(t) = d*(eval(diff(y(x), x), x = t))+k*y(t)
where y(t) is a realy big piecewise function, defined by me.

My initial conditions are:
x(0) = 0, (D(x))(0) = 0

With dsolve, I get the solution x(t) and the first derivative x'(t). I'm able to plot them with odeplot.

But...

Problem 1:
I need also the second derivative x''(t).
On this page: http://www.maplesoft.com/support/help/maple/view.aspx?path=dsolve%2Frkf45there is an example (eq 13 and 14) where the second derivative is useable, but this doesn't work with my differential equation.
(D(D(x)))(0) = 0
to my initial conditions but then, I got the error that only 2 initial conditions are required.
What could I do, so that rkf45 returns also the second derivative?

Problem 2:
And in addition to this, I want to calculate with x(t), x'(t), x''(t) but I found no way to use them.
Only plots are possible.
If I reduce y(t) to a minimum, I can do everything with the analytic solution: plot, d/dt, d2/dt2, +, -, ...
I tried also to convert the procedure to a function but in this case, there is no way to derivate it.

Many thanks...

### Derivative of Spline at the nodes...

August 12 2015
2 4

Hi!

This question is related to http://www.mapleprimes.com/questions/204419-Derivatives-Of-Splines-Are-Not-Defined and http://www.mapleprimes.com/questions/42114-Problem-With-Spline-Integrating , however I have not been able to apply the solutions given there to my problem.

I have a set of points given by

and certain function value points given by

where e1 is the function I am approximating.

Using

I come up with my piecewise function.

When I do diff(e4,x), however, the points at the nodes show "float(undefined) x=0.2..."(the node).

As it turns out, the value of the derivative on the left of the node is not equal to that of the right side by a factor of 10^(-7), in other words, numerically unimportant but high enough for maple to realise it is not the same number. How could I tell Maple that I am happy choosing, for example, the value given by the function on right side of the node?

I welcome any suggestions.

### Alias, surpress or declare with latex outputs...

July 08 2015
2 5

Hello,

i am trying to get a latex output which equals the displayed maple equations, where i am using alias/surpress or declare to shorten the dependencies of my derivatives. Whereas in Maple this looks how i want it to look like, i can not get the latex() command to apply the aliases. Instead it replaces the short forms with the long terms before creating the latex code. Is there anyway to get a latex output directly from the displayed math WITH alias?

2 small examples:

Both yield  $X \left( a,b,c \right)$ whereas i would like to get X. Simply substituing changes the partial differential symbol to "d" in the latex output and makes the equations unuseable, so this is no option i guess..

Thanks a lot for any suggestions!

### Define a derivative operator of fractional order...

June 21 2015
0 4

Dear I want to define a general operator D for Fractional derivative whose behave like this

(D^alpha)(t^beta) = GAMMA(1+beta)*t^(beta-alpha)/GAMMA(1+beta-alpha)

### Derivative from pdsolve/numeric solution?...

June 07 2015
1 12

Is it possible to somehow extract a derivative from numeric solution of partial differential equation?

I know there is a command that does it for dsolve but i couldn't find the same thing for pdsolve.

The actual problem i have is that i have to take a numeric solution, calculate a derivative from it and later use it somewhere else, but the solution that i have is just a set of numbers an array of some sort and i can't really do that because obviously i will get a zero each time.

Perhaps there is a way to interpolate this numeric solution somehow?

I found that someone asked a similar question earlier but i couldn't find an answer for it.

### Derivatives of Splines are not defined on some poi...

June 05 2015
1 2

Hello everyone,

I have a question regarding my Spline interpolations. I am not an expert on the theory there, but the maple help tells me that the first derivative of an 3rd degree spline interpolation should exist at the knots. But a derivation returns "undefined" at some of the knots instead. Here is my example:

x(t):=Spline([[0, 0], [1, 1], [2, 2], [3, 2.2], [4, 1.8]],t,degree=3);

returns

x(t):=piecewise(t < 1, .953571428571429*t+0.464285714285714e-1*t^3, t < 2, -0.9286e-1+1.09285714285714*t+.139285714285714*(t-1)^2-.232142857142857*(t-1)^3, t < 3, .65000+.675000000000000*t-.557142857142857*(t-2)^2+0.821428571428571e-1*(t-2)^3, 2.77857-.192857142857143*t-.310714285714286*(t-3)^2+.103571428571429*(t-3)^3);

diff(x(t),t);

returns

piecewise(t < 1., .953571+.139286*t^2, t = 1., Float(undefined), t < 2., .814286+.278571*t-.696429*(t-1.)^2, t = 2., Float(undefined), t <= 3., 2.90357-1.11429*t+.246429*(t-2.)^2, 3. < t, 1.67143-.621429*t+.310714*(t-3.)^2);

Not defined at t=1 and t=2. Is it possible to get an interpolation of which the first derivative exists at every point? Thank you very much!

### Evaluating with D...

May 19 2015
1 6

I wish to evaluate the expression

knowing that

where a is a constant.  It is not hard to see, assuming enough differentiability,  that the expression evaluates to

I know how to do this when all the derivatives are expressed in terms of the diff() operator.  Here it is:

eq := diff(u(x,t),t) = a^2*diff(u(x,t),x,x);
expr := diff(u(x,t),t,t);
eval['recurse'](expr,[eq]);

However, I would prefer to do the computations when all derivatives are expressed in terms of the D operator but cannot get that to work.  What is the trick?

### I forgot how to turn D or diff into a function......

May 14 2015
0 2

I googled everywhere for this and most results just tell me what diff and D does...

Basically I have a function, let's say

f:= x -> x^2

How do I turn the derivative of f into a function?

I tried

fprime := x -> diff(x^2,x)

But tihs just shows me diff(x^2,x), instead of x -> 2x

### Covariant Derivative and Covariant Tensor and Cont...

May 05 2015
2 4

guys , i have a metric and i want to define a componenets of a tensor and then obtain its covariant derivative with respect to a metric, what is your idea ?

N_1=-A(r)^1/2 , A_2=A_3=A_4=0 , what is D_[nu] N_1 =?

in general i want to define N[1]=-A(r)^(1/2) and N[2] = N[3]= N[3] = N[4] = 0 And define F[mu, nu] = 2*(D_[mu] N[nu]-D_[nu] N[mu]) And define Omega[mu, nu] = 2*(D_[mu] N[nu]+D_[nu] N[mu]) and compute expression F_[alpha, beta] F_[~alpha, ~beta ] And N_[alpha] N_[~beta] F_[ ~alpha, ~lambda ] Omega_[beta, lambda])

i have problem with this how to difine this tensorial terms and how to compute them.

thxxxx

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