I'm guessing not a lot will care about this becasue it's not very relevant, but my calc teacher couldn't do this and I did it in a few seconds, so i'll expose it.(adsbygoogle = window.adsbygoogle || []).push({});

The problem stated that f(x)=x^3+x

and inverse of f(x)=g(x) and g(2)=1

question: Find g'(2)

----------------------------

My teacher tried to create a formula to connect inverse derivative answers and inverse functions for cubics. He couldn't. So while staring at it I realize how the derivative is dy/dx which is appearing everywhere you derivate a y.

so I write y=x^3+x

take inverse x=Y^3+y

and I don't care about what the function looks like. I don't worry about putting it in standard form like he tried. I keep it like this and take derivative. Out of nowhere I might say I had written down 1=3y^2 dy/dx + dy/dx

and isolating the dy/dx => dy/dx = 1/(1+2y^2)

since point (2,1) was given, the fact that I have no x is not important. i can plug in y instead. And I get the final answer. g'(2)=1/4

The relevance of this is that finding the derivative of a function can be expressed in many forms, related to various letters in that expression. many times the y' has both x and y.

But...Standard form was not important here, and pretty much everyone, myslef included for a few minutes were hooked up on putting it in standard form...

I thought i'd share this with you.

~Robokapp

**Physics Forums - The Fusion of Science and Community**

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!

# A handy trick i found

Loading...

Similar Threads for handy trick found | Date |
---|---|

Insights Solve Integrals Involving Tangent and Secant with This One Trick - Comments | Mar 6, 2017 |

I Is there a trick to tell which is the higher curve? | Apr 18, 2016 |

I I found a *useful* method to calculate log(a+b), check it out | Feb 28, 2016 |

Tricks with Excel? | Sep 5, 2015 |

Chain Rule, Differentials "Trick" | Aug 23, 2014 |

**Physics Forums - The Fusion of Science and Community**