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Fp3

http://mathsathawthorn.pbworks.com/f/FP3Jun06.pdf
q3a?
This is what ive done below!
f(x)= lnsecx
x=0 , f(x)=0

f'(x)=tanx
x=0, f'(x)=0

f''(x)=sec^2x
x=0, f''(x)=1

Is f'''(x)=2(sec^2xtanx)

And what is f''''(x)

Reply 1

Student403

You're right about f'''(x).

What have you tried to work out f''''(x)?

Reply 2

Lychee628

Original post by Student403

You're right about f'''(x).

What have you tried to work out f''''(x)?

Well can i use u=sec^2x and v= 2tanx? And find du/dx and dv/dx and cross multiply?

Reply 3

Student403

Original post by Ayaz789

Well can i use u=sec^2x and v= 2tanx? And find du/dx and dv/dx and cross multiply?

cross multiply? I don't see how you could cancel the du and dv. Could you explain how?

Spoiler

Reply 4

Lychee628

Original post by Student403

You're right about f'''(x).

What have you tried to work out f''''(x)?

Or i can do u=2sec^2x and v=tanx as dv/dx =sec^2x but du/dx is?

(edited 7 years ago)

Reply 5

Lychee628

Original post by Student403

cross multiply? I don't see how you could cancel the du and dv. Could you explain how?

Spoiler

Like i do u* dv/dx and v* du/dx

Reply 6

Student403

Original post by Ayaz789

Or i can do u=2sec^x and v=tanx as dv/dx =sec^x but du/dx is?

I'm asking what would you do with du/dx and dv/dx? How do you cancel the du and dv? The substitution doesn't really make sense

Reply 7

Lychee628

Original post by Student403

I'm asking what would you do with du/dx and dv/dx? How do you cancel the du and dv? The substitution doesn't really make sense

I do u* dv/ dx???
And do v* du/ dx??

Reply 8

Student403

Original post by Ayaz789

I do u* dv/ dx???
And do v* du/ dx??

Oh you're talking about the product rule here. Yeah that's fine (sorry)

But remember since you have 2sec²x tanx and you want d/dx (2sec²x tanx), it's better to factor out the 2 to get

2 d/dx (sec²x tanx)

(edited 7 years ago)

Reply 9

the bear

to find the fourth derivative it is sensible to replace sec²(x) with tan²(x) + 1

in the third derivative

Reply 10

Lychee628

Original post by Student403

Oh you're talking about the product rule here. Yeah that's fine

But remember since you have 2sec²x tanx and you want d/dx (2sec²x tanx), it's better to factor out the 2 to get

2 d/dx (sec²x tanx)

Okay can you show me how to get f''''(x)