Derivatives of inverse trigonometric function

Calculus Tutorial

Derivatives of inverse trigonometric function

Intro

the formula for the derivative of arctan(x)=1/(1+x2).

Sample Problem

y=arctan(x/3)
evaluate dy/dx at x=1

Solution

y=arctan(x/3)
dy/dx=d/dx(arctan(x/3) — differentiate
=1/(1+(x/3)2).1/3 — chain rule
=9/(9+x2).1/3 — simlify
=3/(9+x2)
=3/(9+1) — substitute x=1
=3/10



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