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Derivative of BernsteinBasis functions

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  Derivative of BernsteinBasis functions "Rob Y. H. Chai" <yhchai@ucdavis.edu> - 2011-04-23 11:50 +0000

#1847 — Derivative of BernsteinBasis functions

Hello everyone,

I'm trying to compute the second derivative of a function g[x_] that
involves a combination of Bernstein Basis functions. Mathematica version 7 was able to compute the derivative, but version 8 gave a problem. 

In[1]:= {$Version,$ReleaseNumber}

Out[1]= {7.0 for Microsoft Windows (32-bit) (February 18, 2009),1}

In[2]:= g[x_] = -BernsteinBasis[5,0,x]+6 BernsteinBasis[5,1,x]-15
BernsteinBasis[5,2,x]+20 BernsteinBasis[5,3,x]-15 BernsteinBasis[5,4,x]+6
BernsteinBasis[5,5,x]

Out[2]= -BernsteinBasis[5,0,x]+6 BernsteinBasis[5,1,x]-15
BernsteinBasis[5,2,x]+20 BernsteinBasis[5,3,x]-15 BernsteinBasis[5,4,x]+6
BernsteinBasis[5,5,x]

In[3]:= D[g[x],{x,2}]

Out[3]= -20 BernsteinBasis[3,0,x]+30 (-4 BernsteinBasis[3,0,x]-4
(BernsteinBasis[3,0,x]-BernsteinBasis[3,1,x]))-75 (4
(BernsteinBasis[3,0,x]-BernsteinBasis[3,1,x])-4
(BernsteinBasis[3,1,x]-BernsteinBasis[3,2,x]))+100 (4
(BernsteinBasis[3,1,x]-BernsteinBasis[3,2,x])-4
(BernsteinBasis[3,2,x]-BernsteinBasis[3,3,x]))-75 (4
(BernsteinBasis[3,2,x]-BernsteinBasis[3,3,x])-4 BernsteinBasis[3,3,x])+120
BernsteinBasis[3,3,x]

But 

 

{$Version,$ReleaseNumber}

{8.0 for Microsoft Windows (32-bit) (February 24, 2011),1}

 

D[g[x],{x,2}]

 

Gives an error. Any thoughts? 

 

Thanks.

 

Rob Chai

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