compute the first derivative

y=1+arctan(4-5x)

seems easy but i forgot how to find the derivative for arctan so please help

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- Mar 31st 2010, 02:12 PMcalculusphobefind the derivative with arctan
compute the first derivative

y=1+arctan(4-5x)

seems easy but i forgot how to find the derivative for arctan so please help - Mar 31st 2010, 02:15 PMmr fantastic
- Mar 31st 2010, 03:03 PMtom@ballooncalculus
Just in case you don't have this picture in your notes...

http://www.ballooncalculus.org/asy/t...diffArctan.png

... where

http://www.ballooncalculus.org/asy/chain.png

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the present variable (x or theta), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

The general drift...

http://www.ballooncalculus.org/asy/maps/inverse3.png

__Spoiler__:

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!