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Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 QuotientRule

Source Notebook

See how to apply the quotient rule for derivatives to an expression

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["QuotientRule"][f,x]

applies the quotient rule for computing the derivative of f with respect to x, returned as an inactive result.

Details

ResourceFunction["QuotientRule"] accepts the following options:
"PrintRule"Falseprint a statement of the quotient rule
"PrintNapkin"Falseprint the side "napkin" word needed for computing components of the quotient rule
“InactiveInnerDerivatives"Falsekeep the derivatives of the components inactivated

Examples

Basic Examples (1) 

See how to apply the quotient rule to compute the derivative of sin(x) /(8x) with respect to x:

In[1]:=
ResourceFunction["QuotientRule"][Sin[x]/(8 x), x]
Out[1]=

Scope (1) 

In some cases, when there is no explicit quotient in the first argument of QuotientRule, the argument may be interpreted as a quotient:

In[2]:=
ResourceFunction["QuotientRule"][Tan[x], x, "PrintNapkin" -> True]
Out[2]=

Options (3) 

InactiveInnerDerivatives (1) 

Setting "InactiveInnerDerivatives" to True inactivates the derivatives of the factors within the structure of the quotient rule:

In[3]:=
ResourceFunction["QuotientRule"][Log[x]/Tan[x], x, "InactiveInnerDerivatives" -> True]
Out[3]=

PrintNapkin (1) 

Setting "PrintNapkin" to True prints a grid with the side "napkin" work needed to apply the quotient rule (i.e., identifying and computing the derivatives of each factor):

In[4]:=
ResourceFunction["QuotientRule"][x^8/Exp[4 x], x, "PrintNapkin" -> True]
Out[4]=

PrintRule (1) 

Setting "PrintRule" to True prints a general statement of the quotient rule for derivatives:

In[5]:=
ResourceFunction["QuotientRule"][5 x / Cos[x], x, "PrintRule" -> True]
Out[5]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 2.0.0 – 23 March 2023
  • 1.0.0 – 08 February 2023

Related Resources

Author Notes

To view the full source code for QuotientRule, evaluate the following:

License Information