Compute Difference Quotients: New In Wolfram Language 11

‹›Symbolic & Numeric Calculus

Compute Difference Quotients

The Wolfram Language can compute not only the well-known univariate difference quotient, but multivariate and higher-order quotients as well.

In[1]:=DifferenceQuotient[f[x], {x, h}]Out[1]=

The second-order difference quotient is the difference quotient of the first-order quotient.

In[2]:=DifferenceQuotient[f[x], {x, 2, h}]Out[2]=In[3]:=DifferenceQuotient[f[x], {x, h}]; DifferenceQuotient[f[x], {x, 2, h}]; % == DifferenceQuotient[%%, {x, h}]Out[3]=

Compute a multivariate difference quotient.

In[4]:=DifferenceQuotient[(x + y + 1)/(((x^2 + 3) (y + 5))), {x, h}, {y, k}]Out[4]=

Create a table of increasing difference quotients of a polynomial, which produces polynomials of decreasing order.

In[5]:=Grid[Table[ DifferenceQuotient[x^3 y^2 + 5 x y + 11, {x, i, r}, {y, j, s}], {i, 4}, {j, 3}], Spacings -> {2, 1}]Out[5]=

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