gives the derivative of the Scorer function
.
ScorerGiPrime
gives the derivative of the Scorer function
.
Details
- Mathematical function, suitable for both symbolic and numeric manipulation.
- For certain special arguments, ScorerGiPrime automatically evaluates to exact values.
- ScorerGiPrime can be evaluated to arbitrary numerical precision.
- ScorerGiPrime automatically threads over lists.
- ScorerGiPrime can be used with Interval and CenteredInterval objects. »
Examples
open all close allBasic Examples (4)
ScorerGiPrime[5.]Plot over a subset of the reals:
Plot[ScorerGiPrime[x], {x, -10, 3}]Plot over a subset of the complexes:
ComplexPlot3D[ScorerGiPrime[z], {z, -2 - 2I, 2 + 2I}, PlotLegends -> Automatic]Series expansion at the origin:
Series[ScorerGiPrime[x], {x, 0, 4}]//FullSimplifyScope (31)
Numerical Evaluation (6)
ScorerGiPrime[25.]N[ScorerGiPrime[Pi / 2]]N[ScorerGiPrime[1 / 3], 50]The precision of the output tracks the precision of the input:
ScorerGiPrime[0.312785550000555523000]ScorerGiPrime[0.2 + I]N[ScorerGiPrime[I Pi / 3]]Evaluate efficiently at high precision:
N[ScorerGiPrime[Pi / 3`100]]//TimingN[ScorerGiPrime[Pi / 3`10000]];//TimingCompute worst-case guaranteed intervals using Interval and CenteredInterval objects:
ScorerGiPrime[Interval[{0.77, 0.78}]]ScorerGiPrime[CenteredInterval[2, 1 / 1000]]Or compute average-case statistical intervals using Around:
ScorerGiPrime[Around[.9, 0.1]]Compute the elementwise values of an array:
ScorerGiPrime[{{1.3, .5}, {0, 0.2}}]Or compute the matrix ScorerGiPrime function using MatrixFunction:
MatrixFunction[ScorerGiPrime[#]&, {{1.3, .5}, {0, 0.2}}]Specific Values (3)
Simple exact values are generated automatically:
ScorerGiPrime[0]Limit[ScorerGiPrime[x], x -> Infinity]Find positive minimum of ScorerGiPrime[x ]:
xmax = x /. FindRoot[D[ScorerGiPrime[x ], x] == 0, {x, 2}]Plot[ScorerGiPrime[x ], {x, 0, 5}, Epilog -> Style[Point[{xmax, ScorerGiPrime[xmax ]}], PointSize[Large], Red]]Visualization (2)
Plot the ScorerGiPrime function:
Plot[ScorerGiPrime[x], {x, -10, 4}]ComplexContourPlot[Re[ScorerGiPrime[z]], {z, -4 - 4I, 4 + 4I}, Contours -> 24]ComplexContourPlot[Im[ScorerGiPrime[z]], {z, -4 - 4I, 4 + 4I}, Contours -> 24]Function Properties (11)
Real domain of ScorerGiPrime:
FunctionDomain[ScorerGiPrime[x], x]FunctionDomain[ScorerGiPrime[z], z, Complexes]Function range of ScorerGiPrime:
FunctionRange[ScorerGiPrime[x], x, y]//QuietScorerGiPrime threads elementwise over lists:
ScorerGiPrime[{-1., 1., 2.}]ScorerGiPrime is an analytic function of x:
FunctionAnalytic[ScorerGiPrime[x], x]ScorerGiPrime is neither nondecreasing nor nonincreasing:
FunctionMonotonicity[ScorerGiPrime[x], x]ScorerGiPrime is not injective:
FunctionInjective[ScorerGiPrime[x], x]Plot[{ScorerGiPrime[x], 0.3}, {x, -10, 10}]ScorerGiPrime is surjective:
FunctionSurjective[ScorerGiPrime[x], x]Limit[ScorerGiPrime[x], x -> -∞]ScorerGiPrime is neither non-negative nor non-positive:
FunctionSign[ScorerGiPrime[x], x]FunctionSign[ScorerGiPrime[x], x]ScorerGiPrime does not have singularity or discontinuity:
FunctionSingularities[ScorerGiPrime[x], x]FunctionDiscontinuities[ScorerGiPrime[x], x]ScorerGiPrime is neither convex nor concave:
FunctionConvexity[ScorerGiPrime[x], x]TraditionalForm typesetting:
ScorerGiPrime[z]//TraditionalFormDifferentiation and Integration (4)
First derivative with respect to z:
D[ScorerGiPrime[z] , z]Higher derivatives with respect to z:
Table[D[ScorerGiPrime[z], {z, k}], {k, 1, 3}]//SimplifyPlot the higher derivatives with respect to z:
Plot[%, {z, -5, 5}, PlotLegends -> {"First Derivative", "Second Derivative", "Third Derivative"}]Formula for the ![]()
derivative with respect to z:
D[ScorerGiPrime[z], {z, k}]// FullSimplifyIndefinite integral of ScorerGiPrime:
Integrate[ScorerGiPrime[x], x]Series Expansions (2)
Find the Taylor expansion using Series:
Series[ScorerGiPrime[x], {x, 0, 3}]Series[ScorerGiPrime[x], {x, 0, 3}]Plots of the first three approximations around
:
terms = Normal@Table[Series[ScorerGiPrime[x], {x, 0, m}], {m, 1, 5, 2}];
Plot[{ScorerGiPrime[x], terms}, {x, -10, 10}]Taylor expansion at a generic point:
Series[ScorerGiPrime[x], {x, x0, 2}]// FullSimplifyFunction Identities and Simplifications (3)
FunctionExpand tries to simplify the argument of ScorerGiPrime:
FunctionExpand[ScorerGiPrime[z E^2 π I]]//SimplifyFunctionExpand[ScorerGiPrime[(z^2)^1 / 2]]//SimplifyScorerGiPrime[z] + E^2 π I ScorerGiPrime[z E^2 π I] + E^-2 π I ScorerGiPrime[z E^-2 π I]//FullSimplifyScorerGiPrime can be represented as a DifferentialRoot:
DifferentialRootReduce[ScorerGiPrime[x], x]See Also
Related Guides
History
Text
Wolfram Research (2014), ScorerGiPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/ScorerGiPrime.html.
CMS
Wolfram Language. 2014. "ScorerGiPrime." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ScorerGiPrime.html.
APA
Wolfram Language. (2014). ScorerGiPrime. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ScorerGiPrime.html
BibTeX
@misc{reference.wolfram_2026_scorergiprime, author="Wolfram Research", title="{ScorerGiPrime}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/ScorerGiPrime.html}", note=[Accessed: 12-June-2026]}
BibLaTeX
@online{reference.wolfram_2026_scorergiprime, organization={Wolfram Research}, title={ScorerGiPrime}, year={2014}, url={https://reference.wolfram.com/language/ref/ScorerGiPrime.html}, note=[Accessed: 12-June-2026]}