Question

what is the derivative of 1/sec^2 3x(tan^2 3x - 1)

Answer 1

I'm going to write tangent squared of 3x as
(tan (3x))^2
The derivative will be found using the chain rule
(d/dx) (tan (3x))^2
= 2(tan (3x)) (tan (3x))'
= 2(tan (3x)) (sec (3x))^2 (3x)'
= 2(tan (3x)) (sec (3x))^2 (3)
= 6(tan (3x)) (sec (3x))^2

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