what is derivative of (ln(2tanx))^2?

Answer 1

Use the chain rule:

First, the derivative of 2tan(x) = 2sec^2(x)
Next, the derivative of ln(y) = 1/y, so we get 1/[2tan(x)] for that.
And finally, apply the power rule.

All together, we have

2 * (ln[2tan(x)]) * 2sec^2(x) / 2tan(x)
2 * (ln[2tan(x)]) * sec^2(x) / tan(x) <--Gopal agrees with this

sec^2(x) / tan(x) can be simplified. Let's write it as

(1 / cos^2(x)) * cos(x) / sin(x) = 1 / cos(x)sin(x)

final answer:

2 * ln{2tan(x)] / cos(x)sin(x)

OpenPsych has the denominator wrong. The wrong denominator conveniently cancels out. The denominator should be as I have it, not ln[2tan(x)]. OpenPsych has an extra "ln."

Answer 2

it is 2 ln(2tanx)*1/2tanx(2sec^x)
=2sec^2x*ln(2tanx)/tanx

Answer 3

i won't give an answer... but ln(a^n) = n ln(a)
it could help

Answer 4

y=[ln(2tanx)]^2
y'
=2*[ln(2tanx)]*[1/ln[2tanx]]
*2*sec^2x
=4sec^2x