Question

Differentiate f(x)=secx/ 1+secx

I used quotient rule and so far I have
F'(x)= secxtanx(1+secx) - (secx)(secxtanx)

Step by step after this would be appreciated ! I thought I would multiply the secx and get

Sec^2xtanx - sec^2xtanx

Someone help please:(

Answer 1

\[f(x)=\frac{\sec x}{1+\sec x}=\frac{1/\cos x}{1+1/\cos x}=\frac{1}{1+\cos x}\\
f'(x)=\frac{1+\cos x+\sin x}{(1+\cos x)^2}\]

Answer 2

The answer in the back of the book says secxtanx / (1+secx)^2 though

Answer 3

I figured it out ! Wooo!

Answer 4

Thank you for responding !!

Answer 5

Ok ;)