quotient rule A2

economist2

19

can sum1 show me how to get d/dx 1/cosx=secx tanx using quotient rule? :smile:

Reply 1

user2020user

16

Original post by economist2

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Do you know the quotient rule?

\dfrac{\text{d}}{\text{d}x} \left( \dfrac{u}{v} \right) = \dfrac{vu' - uv'}{v^2}

(edited 9 years ago)

Reply 2

Usey11

u = 1
Du/dx = 0

v = cos x
dv/dx = -sin x

Quotient rule:
(v*Du/dx - u*dv/dx)/v²
v*Du/dx = 0
u*dv/dx = -sin x
v² = cos² x

(0 - - sin x)/cos² x = sin x / cos² x = (sin x/ cos x) * (1/cos x) = tan x * sec x

(edited 9 years ago)

Reply 3

economist2

OP

19

Original post by Usey11

u = 1
Du/dx = 0

v = cos x
dv/dx = -sin x

Quotient rule:
(v*Du/dx - u*dv/dx)/v²
v*Du/dx = 0
u*dv/dx = -sin x
v² = cos² x

(0 - - sin x)/cos² x = sin x / cos² x = (sin x/ cos x) * (1/cos x) = tan x * sec x

thanks you very much.I forgot to multiply 0 with cosx in vdu/dx....yes,very stupid of me...

Reply 4

economist2

OP

19

Original post by Khallil

Do you know the quotient rule?

\dfrac{\text{d}}{\text{d}x} \left( \dfrac{u}{v} \right) = \dfrac{vu' - uv'}{v^2}

why would'nt I?I could just google it(not that I need to :cool:

).

Reply 5

user2020user

16

Original post by economist2

...

Do you know how to derive the quotient and product rules? :wink:

(edited 9 years ago)

Reply 6

economist2

OP

19

Original post by Khallil

Do you know how to derive the product rule? :wink:

yes.help me out on this one...

y = ln(sec x + tan x)

show that dy/dx = secx

Reply 7

user2020user

16

Original post by economist2

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It's merely an exercise in applying the chain rule of differentiation.

\dfrac{\text{d}}{\text{d}x} \log f(x) = \dfrac{f'(x)}{f(x)}

Do you know how to derive them using first principles and/or logarithms? :ahee:

(edited 9 years ago)

Reply 8

economist2

OP

19

Original post by Khallil

It's merely using the chain rule of differentiation:

\dfrac{\text{d}}{\text{d}x} \log f(x) = \dfrac{f'(x)}{f(x)}

Do you know how to derive them using first principles and/or logarithms? :ahee:

ay.stop with the complicated mathematical terms.I dont need that stuff. :cool:

Reply 9

user2020user

16

Original post by economist2

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It isn't complicated at A Level. First principles are the basics of differentiation and should be covered at AS.

Reply 10

economist2

OP

19

Original post by Khallil

It isn't complicated at A Level. First principles are the basics of differentiation and should be covered at AS.

I self tutored myself.I probably only know the basic terms.I'm capable of doing most sums despite this.After my exam tomorrow(A2) I probably wont need maths anymore,so learning the terms isnt necessary for me.

PS I'm not going to be an economist. :colone:

Reply 11

user2020user

16

Original post by economist2

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The two don't go together. Surely an economist must need maths!

Reply 12

economist2

OP

19

Original post by Khallil

The two don't go together. Surely an economist must need maths!

you read the ps right?when I picked the username,I had other thoughts....now,I'm going to study ACCA after I'm done with Alevels(not much math needed)....