# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Get the derivative with respect to a function

Contributed by:
Carl Woll

ResourceFunction["ChainD"][ gives the partial derivative of | |

ResourceFunction["ChainD"][ gives the | |

ResourceFunction["ChainD"][ gives the partial derivative of |

Only derivatives with respect to univariate functions are supported.

When differentiating with respect to multiple functions, each function must be a univariate function, but they need not be functions of the same variable.

Derivatives with respect to different functions are, in general, not commutative.

A symbolic inverse of the function *g*(*x*) is not required.

Derivatives with respect to functions are obtained using the relation .

Derivative of *x*^{4} with respect to *x*^{2}:

In[1]:= |

Out[1]= |

Derivative of a more complicated function:

In[2]:= |

Out[2]= |

It is not necessary to be able to symbolically invert *g*(*x*):

In[3]:= |

Out[3]= |

It is not possible to symbolically invert BesselJ[2,*x*]:

In[4]:= |

Out[4]= |

Derivative of a multivariate function with respect to functions of each of the variables:

In[5]:= |

Out[5]= |

When using ChainD with multiple functions, the result in general depends on the order of derivatives:

In[6]:= |

Out[6]= |

In[7]:= |

Out[7]= |

Derivatives with respect to heads of functions are not supported:

In[8]:= |

Out[8]= |

- 2.0.0 – 28 February 2020
- 1.0.0 – 23 October 2019

This work is licensed under a Creative Commons Attribution 4.0 International License