Question

What is the 2nd derivative of y=tanx?

Answer 1

I would use the Quotient Rule (twice):

Answer 2

`d/(dx)(tanx) = sec^2 x` note this is `=(secx)^2`

`d/(dx)(secx)=sec x tanx`,
and `d/(dx)(u^2) = 2u (du)/(dx)`so

`d^2/(dx^2)(tanx) = d/(dx)(sec^2x) = 2secx (secxtanx)`

Simplifying, gives:
`d^2/(dx^2)(tanx) = 2sec^2 x tanx`