Thread: find 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

Originally Posted by calculusphobe

compute the first derivative
y=1+arctan(4-5x)

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

The cure for forgetfullness in this instance is to go to your classnotes, textbook or use Google.

Just in case you don't have this picture in your notes...



... where



... 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...

Spoiler:

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!