Question

what's the derivative of tan^-1 (lnx)

Answer 1

1/[x*{1+(lnx)^2}]

Answer 2

what happened to the tan function?

Answer 3

thats tan inverse, isnt it?

Answer 4

I believe so. I read a negative sign on a trig function is an inverse and not a fractional exponent

Answer 5

It is inverse otherwise the power should be after the ln(x).

Answer 6

hmm.. derivative of tan inverse x is 1/(1+x^2)
so, here replace x with ln x and apply chain rule.

Answer 7

Ok. I keep forgetting the how the chain rule works. Can you please explain it.

Answer 8

at first, differenciate the tan inverse function
then differenciate the ln x, thats 1/x
multiply both