Question

Find f prime (x) if f(x) = (cosx)/(1+secx)

Answer 1

have you tried quotient rule?

Answer 2

Yes, I did and then I don't know how to distribute? I know I have to use it It just doesn't fully come out

Answer 3

Show us how far you got with the quotient rule. Show all the steps you have so far. Can you do that?

Answer 4

Yes, I get (

Answer 5

Correct! So far! Now what do you think the next step should be to simplify?

Answer 6

You're only going to simplify the numerator. Never expand the denominator. Do you understand?

Answer 7

Yes. Should I distribute the -sinx to (1+secx)?

Answer 8

Go ahead and apply the distributive property to the numerator. In other words, expand.

Answer 9

Yes! Go ahead. Show me the next step.

Answer 10

I shouldn't distribute the cosx correct? Because tanx and secx are being multiplied together?

Answer 11

Yes expand the entire numerator. Meaning I shouldn't see any more parentheses in the numerator. Go ahead!

Answer 12

After that change each sec x to 1/cos x. Understood? Go ahead.

Answer 13

I mean change each sec x to 1/cos x only in the numerator. Never expand the denominator, like I said earlier. Do you understand?

Answer 14

Yes. I am just confused on what I should do to the -cosx(tanxsecx)

Answer 15

\[-\cos x(\tan x \sec x)=-(\cos x)(\tan x)(\frac{ 1 }{ \cos x })\]Agreed?

Answer 16

So do exactly that. Go ahead.

Answer 17

Now show me the step in it's entirety.

Answer 18

Okay.