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Advanced Higher Mathematics Help Watch

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    Hi,

    Can someone help me with the questions stated below please. I have done some working but I am finding it difficult when it comes to taking out a common factor/simplifying to match the answer in the book.

    Calculate dy/dx for:

    1. y = sec x tan x
    2. y = cot (tan x )
    3. y = cosec(sin x)

    My working so far:

    1. y = sec x tan x
    dy/dx = secx . sec^2x + tanx . secxtanx
    = sec^3x + tanx . secxtanx
    = secx ( sec^2x + tan^2x)
    = secx(1/cos^2x + sin^2x/cos^2x)
    = secx(1 + sin^2x+/cos^2x )
    = ...

    Answer in the book = sec x (2 sec^2x - 1)
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    (Original post by kurt123)
    Hi,

    Can someone help me with the questions stated below please. I have done some working but I am finding it difficult when it comes to taking out a common factor/simplifying to match the answer in the book.

    Calculate dy/dx for:

    1. y = sec x tan x
    2. y = cot (tan x )
    3. y = cosec(sin x)

    My working so far:

    1. y = sec x tan x
    dy/dx = secx . sec^2x + tanx . secxtanx
    = sec^3x + tanx . secxtanx
    = secx ( sec^2x + tan^2x)
    = secx(1/cos^2x + sin^2x/cos^2x)
    = secx(1 + sin^2x+/cos^2x )
    = ...

    Answer in the book = sec x (2 sec^2x - 1)
    Are you familiar with this identity

    1 + (tanx)^2 = (secx)?

    Use this to replace the (tanx)^2 part I put I bold I for quote above ^.
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    (Original post by kurt123)
    Hi,

    Can someone help me with the questions stated below please. I have done some working but I am finding it difficult when it comes to taking out a common factor/simplifying to match the answer in the book.

    Calculate dy/dx for:

    1. y = sec x tan x
    2. y = cot (tan x )
    3. y = cosec(sin x)

    My working so far:

    1. y = sec x tan x
    dy/dx = secx . sec^2x + tanx . secxtanx
    = sec^3x + tanx . secxtanx
    = secx ( sec^2x + tan^2x)
    = secx(1/cos^2x + sin^2x/cos^2x)
    = secx(1 + sin^2x+/cos^2x )
    = ...

    Answer in the book = sec x (2 sec^2x - 1)
    You should know a rule that connects \sec^2x and \tan^2x
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    (Original post by krisshP)
    Are you familiar with this identity

    1 + (tanx)^2 = (secx)?

    Use this to replace the (tanx)^2 part I put I bold I for quote above ^.
    No, I only started the course 2 days ago.
    However , I was told secx = 1/cosx
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    (Original post by TenOfThem)
    You should know a rule that connects \sec^2x and \tan^2x
    This might actually be in the A. Higher formula book.
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    (Original post by TenOfThem)
    You should know a rule that connects \sec^2x and \tan^2x
    Is it 1 + tan^2x = sec^2x
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    (Original post by kurt123)
    No, I only started the course 2 days ago.
    However , I was told secx = 1/cosx
    Do you know this:

    (Sinx)^2 + (Cosx)^2 =1

    ?

    Divide both sides by (cosx)^2 and see what you get.

    Another identity can be obtained if divide both sides by (sinx)^2

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    (Original post by krisshP)
    Do you know this:

    (Sinx)^2 + (Cosx)^2 =1

    ?

    Divide both sides by (cosx)^2 and see what you get.

    Another identity can be obtained if divide both sides by (sinx)^2


    Yep, from Higher

    should I take it from the line:
    secx (sec^2x + tan^2x)
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    (Original post by kurt123)
    Yep, from Higher

    should I take it from the line:
    secx (sec^2x + tan^2x)
    Really I don't remember doing this at higher, then again it was a while ago now.
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    (Original post by kurt123)
    Is it 1 + tan^2x = sec^2x
    Yes

    It comes from

    \sin^2 x + \cos^2 x = 1

    If you divide this by \cos^2x or by \sin^2 x you get 2 really useful identities

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    (Original post by kurt123)
    Yep, from Higher

    should I take it from the line:
    secx (sec^2x + tan^2x)
    Yep
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    (Original post by TenOfThem)
    Yes

    It comes from

    \sin^2 x + \cos^2 x = 1

    If you divide this by \cos^2x or by \sin^2 x you get 2 really useful identities

    (Original post by krisshP)
    Yep

    Thanks very much. Finally got it.
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    For 2. y = cot(tanx) my working so far is:

    dy/dx = cot . sec^2x + tanx . -cosec^2
    = 1/tan . sec^2x - tanxcosec^2

    Where would I go from there if that's correct?
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    (Original post by kurt123)
    For 2. y = cot(tanx) my working so far is:

    dy/dx = cot . sec^2x + tanx . -cosec^2
    = 1/tan . sec^2x - tanxcosec^2

    Where would I go from there if that's correct?
    This one is chain rule not product rule
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    (Original post by kurt123)
    For 2. y = cot(tanx) my working so far is:

    dy/dx = cot . sec^2x + tanx . -cosec^2
    = 1/tan . sec^2x - tanxcosec^2

    Where would I go from there if that's correct?
    Use the substitution u= tan(x)
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    (Original post by zaback21)
    Use the substitution u= tan(x)
    (Original post by TenOfThem)
    This one is chain rule not product rule
    Thanks!

    How do you know when to use the chain rule and product rule?
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    (Original post by kurt123)
    Thanks!

    How do you know when to use the chain rule and product rule?
    Because it is the function of a function not a function multiplied by a function
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    (Original post by kurt123)
    Thanks!

    How do you know when to use the chain rule and product rule?
    When I was taught these, a good way we were taught to remember was that the product rule is as such a product (multiplication) of two functions. The chainrule on the otherhand is implemented when there is a function of a function i.e. derivative of f(g(t)). Sometimes you even have to implement both perhaps when caluclating the derivative of a product where one or more of the functions of the product has a function inside.
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    (Original post by TenOfThem)
    Because it is the function of a function not a function multiplied by a function
    (Original post by BAD AT MATHS)
    When I was taught these, a good way we were taught to remember was that the product rule is as such a product (multiplication) of two functions. The chainrule on the otherhand is implemented when there is a function of a function i.e. derivative of f(g(t)). Sometimes you even have to implement both perhaps when caluclating the derivative of a product where one or more of the functions of the product has a function inside.
    Thanks for the help.
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    I know partial fractions are meant to be easy but I am stuck on 2 questions.

    Express each of the following in partial fractions.

    1) 3x+1 / (x - 1) (x^2 - 1)

    2) 3x + 3 / (x - 1) (x^2 + x +1)



    Any help would be much appreciated.
 
 
 
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