 Differentiate - Maple Help

DifferentialAlgebra[Tools]

 Differentiate
 differentiates a differential rational fraction Calling Sequence Differentiate(p, theta, R, opts) Differentiate(L, theta, R, opts) Differentiate(ideal, theta, opts) Parameters

 p - a differential rational fraction L - a list or a set of differential polynomials or rational fractions theta - a sequence of derivation operators R - a differential polynomial ring or ideal ideal - a differential ideal opts (optional) - a sequence of options Options

 • The opts arguments may contain one or more of the options below.
 • fullset = boolean. In the case of the function call Differentiate(ideal,theta), applies the function also over the differential polynomials which state that the derivatives of the parameters are zero. Default value is false.
 • notation = jet, tjet, diff or Diff. Specifies the notation used for the result of the function call. If not specified, the notation of p is used.
 • memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero (no memory out). Description

 • The function call Differentiate(p, theta, R) returns the derivative of p with respect to theta. The parameter p is regarded as a differential polynomial or a differential rational fraction of R, or of its embedding ring if R is an ideal.
 • The parameter theta is a possibly empty sequence of differential operators. See DifferentialAlgebra for more details.
 • The function call Differentiate(L, theta, R) returns the list or the set of the derivatives of the elements of L with respect to theta.
 • If ideal is a regular differential chain, the function call Differentiate(ideal, theta) returns the list of the derivatives of the chain elements. If ideal is a list of regular differential chains, the function call returns a list of lists of derivatives.
 • This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form Differentiate(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][Differentiate](...). Examples

 > $\mathrm{with}\left(\mathrm{DifferentialAlgebra}\right):$$\mathrm{with}\left(\mathrm{Tools}\right):$
 > $R≔\mathrm{DifferentialRing}\left(\mathrm{derivations}=\left[t\right],\mathrm{blocks}=\left[u\right]\right)$
 ${R}{≔}{\mathrm{differential_ring}}$ (1)
 > $\mathrm{Differentiate}\left({u}_{t}^{2}-4u,t,R\right)$
 ${2}{}{{u}}_{{t}}{}{{u}}_{{t}{,}{t}}{-}{4}{}{{u}}_{{t}}$ (2)
 > $\mathrm{Differentiate}\left(\left[u,\frac{1}{u}\right],{t}^{2},R\right)$
 $\left[{{u}}_{{t}{,}{t}}{,}\frac{{-}{{u}}^{{2}}{}{{u}}_{{t}{,}{t}}{+}{2}{}{u}{}{{u}}_{{t}}^{{2}}}{{{u}}^{{4}}}\right]$ (3)

No differential operator is provided. The function acts as the identity.

 > $\mathrm{Differentiate}\left({u}_{t}^{2}-4u,\mathrm{notation}=\mathrm{diff},R\right)$
 ${\left(\frac{{ⅆ}}{{ⅆ}{t}}\phantom{\rule[-0.0ex]{0.4em}{0.0ex}}{u}{}\left({t}\right)\right)}^{{2}}{-}{4}{}{u}{}\left({t}\right)$ (4)