Turn on thread page Beta
    • Thread Starter

    Y= 7x(Cosx)^(x/2)


    1- Ln both sides

    Working on the RHS first


    2. Then "Expand the bracket" using logaritmic rules=

    Ln(7x) +Ln(Cosx)^(x/2)

    3. Now, Bring down the power in the second term to the front

    Ln(7x) + (x/2)Ln Cosx

    4. Differenriate as usual with respect to x

    First term

    Ln(7x) = 1/(7x)

    For the Second term

    (X/2) LnCos X

    Use the product rule and the chain rule because there are 2 functions being multiplied and an inner and outer function.

    Using the product rule to differentiate (x/2)Ln Cosx

    U= x/2 V= lnCosx

    U'v +V'u=

    (X/2) (LnCosx')+ LnCosx(X/2')

    Differentiating LnCos x requires the Chain rule

    = (1/Cosx)* -Sinx
    Since sinx/cosx = Tan x, -(sinx/cosx) = -tanx

    second term (of the product rule) - derivative of x/2= 1/2

    So together we have:




    4. Working on the LHS now

    Lny=( 1/y)dy/dx

    Therefore the whole thing is:

    (1/Y)dy/dx= -Tanx+Lncosx/2

    Multiplying both sides by y we get:

    Dy/dx= Y *( -Tanx+Lncosx/2)

    Substituting the value of Y from the equation

    Recall: Y= 7x(cosx)^(x/2)

    Therefore dy/dx=

    7x(cosx)^(x/2)* ((-Tanx+Lncosx)/2)

    Please can anyone check this for me, I would be ever so grateful!! 😊😊😊
    • Community Assistant

    Community Assistant
    (Original post by FloralEssence)
    No that's not right. Also PLEASE use LaTex or clearer representation, there's a lot of ambiguity there.

    \frac{d}{dx}(\ln \lvert 7x \lvert )=\frac{1}{x}\not= \frac{1}{7x}

    and when you say "the whole thing is..." you are missing the derivative I corrected above.

    \frac{d}{dx}(\frac{x}{2} \ln\lvert \cos x \lvert ) is correct though.

    ALSO please do not say \ln(7x) = \frac{1}{7x} as it doesn't make sense when you're actually differentiating it...

    (the more i look through this the more errors i seem to find)
Submit reply
Turn on thread page Beta
Updated: February 1, 2017
Favourite type of bread
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.