Question #de32c

1 Answer
Oct 29, 2017

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

Explanation:

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)