Here was my thinking for differentiation (which, by the way, is wrong):(adsbygoogle = window.adsbygoogle || []).push({});

By the definition of the function, the following equations are equal:

$$W(xe^x)=x$$

By the chain rule and product rule:

$$\frac{dW}{dx}( e^x+xe^x ) =1$$

$$\frac{dW}{dx}=(e^x+xe^x)^{-1}$$

What is the error here? What is the correct way to differentiate it? Also, how would I integrate it?

P.S. Why is the fraction bar in the third equation bolder than in the second equation? They are typesetted the same way...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Differentiating and Integrating the Lambert W function

Loading...

Similar Threads for Differentiating Integrating Lambert |
---|

B When do we use which notation for Delta and Differentiation? |

B Product rule OR Partial differentiation |

A Differential operator, inverse thereof |

I Differentiation of sin function where's my mistake? |

A Integration by parts of a differential |

**Physics Forums | Science Articles, Homework Help, Discussion**