Question

Given that the integral of g(x)dx = ln|secx+tanx|+ c Find g(x)

Answer 1

\[\int\limits_{}^{}g(x) dx = \ln \left| secx+tanx \right| + c\]

Answer 2

differentiate both sides with respect to x.

Answer 3

I see that in my notes but I don't understad it

Answer 4

its secx

Answer 5

when I get to the part
g(x)= \[\frac{ d }{ dx } \ln|secx+tanx|\]
what do I do

Answer 6

like how do I differentiate it, what's the formula

Answer 7

just a minute...

Answer 8

chain rule
d(ln u)/dx = (1/u) (du/dx)

Answer 9

\[d/dx (\ln \left| secx+tanx \right|)\]
\[(1/\left| secx+tanx \right|)(\left| secx+tanx \right|/(secx+tanx))(secxtanx+\sec ^{2}x)\]

Answer 10

\[(\sec(x)\tan(x)+\sec ^{2}x)/(\sec(x)+\tan(x))\]
\[\sec(x)(\sec(x)+\tan(x))/(\sec(x)+\tan(x))\]
sec(x)

Answer 11

Ah!!!!! okay!! thank you!

Answer 12

firstly i have used the formula...
d/dx(ln x)=1/x
\[d/dx(\left| x \right|)=\left| x \right|/x\]
d/dx(secx)=secx tanx
d/dx(tanx)=sec^2(x)