Question #de32c

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Answer 1 · 2017-10-29T20:59:30

#dy/dx = 3/(1+9x^2)#

We can compute the differential using implicit differentiation;

if # y = tan^-1 3x #
then; # tany = 3x #

Differentiate implicitly;

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

As using the standard result #d/dx(tanx) = sec^2x#

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

Now by considering how #1+tan^2y = sec^2y # for # y in RR#

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

Hence #dy/dx = 3/(1+9x^2)#