Question

Find f'(x) for f(x) = arcsec(x/2)

Answer 1

Substitute u = x/2 into this equation:
\[D _{x} \sec^-1 u = \frac{ 1 }{ u \sqrt{u^2-1} }D _{x} u\]

Answer 2

I hope that helps

Answer 3

That would make it \[\frac{ 1 }{ \frac{ x }{ 2 } \sqrt{(\frac{ x }{ 2 })^{2}-1}} \times \frac{ 1 }{ 2 }\] right? I'm just not sure how to go about simplifying this.

Answer 4

\[\frac{ 1 }{ \frac{ x }{2 } \times \frac{ 1 }{ 2 } \sqrt{x^2 - 4}} \times \frac{ 1 }{ 2 }\]

Answer 5

Then the 1/2 on the right cancels out with the 1/2 next to the radical

Answer 6

Ah, alright. Thank you very much.