What is the derivative of this function #y=tan^-1(3x)#?

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Answer 1 · 2016-12-13T16:36:27

The answer is #=3/(1+9x^2)#

#y=tan^(-1)3x#

#:.tany=3x#

Differentiating

#sec^2y dy/dx=3#

#dy/dx=3/sec^2y=3cos^2y#

#sin^2y+cos^2y=1#

#tan^2y+1=sec^2y#

#sec^2y=1+9x^2#

#cos^2y=1/(1+9x^2)#

#:.dy/dx=3cos^2y=3/(1+9x^2)#