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isdifferentiable

test for piecewise functions

 Calling Sequence isdifferentiable(expr, var, class) isdifferentiable(expr, var, class, varparam)

Parameters

 expr - expression var - variable name class - number n telling if the expr is in class ${C}^{n}$ varparam - (optional) name

Description

 • isdifferentiable determines if the expression expr containing piecewise or piecewise functions such as abs, signum, max, ..., is of class $C^$ class.  It returns either true or false.
 • The optional argument varparam can be passed to the function and in case expr is not of class ${C}^{n}$, varparam contains information of which ${C}^{n}$ class the function is, and a list of points where we have discontinuities in the n+1-th derivative.

Examples

 > $\mathrm{piecewise}\left(x<-1,-x,x<1,xx,x\right)$
 $\left\{\begin{array}{cc}{-}{x}& {x}{<}{-1}\\ {{x}}^{{2}}& {x}{<}{1}\\ {x}& {\mathrm{otherwise}}\end{array}\right\$ (1)
 > $\mathrm{isdifferentiable}\left(,x,1\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{isdifferentiable}\left(,x,2,'\mathrm{la}'\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{la}$
 ${0}{,}\left\{{-1}{,}{1}\right\}$ (4)
 > $\mathrm{isdifferentiable}\left(\mathrm{abs}\left(x\right),x,2\right)$
 ${\mathrm{false}}$ (5)
 > $\mathrm{isdifferentiable}\left(\mathrm{abs}\left(x\right),x,2,'\mathrm{la}'\right)$
 ${\mathrm{false}}$ (6)
 > $\mathrm{la}$
 ${0}{,}\left\{{0}\right\}$ (7)

 See Also