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