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    Hey, I'm really struggling with the harder differentiating questions in C1

    I can do ones such as 5x^3+7x+3 (15x^2+7)

    But the following ones, I really don't understand where to even start

    1) Differentiate with respect to x

    a) (x+4)^2/x

    2) The curve C has the equation y=4x^2 + 5-x/x where x cannot equal 0. The point P on C has x coordinate 1

    a) Show that the value of dy/dx at P is 3
    b)Find an equation of the tangent to C at P

    The tangent meets the x-axis at (k,0)
    c)Find the value of K
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    (Original post by Bevin)
    Hey, I'm really struggling with the harder differentiating questions in C1

    I can do ones such as 5x^3+7x+3 (15x^2+7)

    But the following ones, I really don't understand where to even start

    1) Differentiate with respect to x

    a) (x+4)^2/x

    2) The curve C has the equation y=4x^2 + 5-x/x where x cannot equal 0. The point P on C has x coordinate 1

    a) Show that the value of dy/dx at P is 3
    b)Find an equation of the tangent to C at P

    The tangent meets the x-axis at (k,0)
    c)Find the value of K

    For 1a

    Expand the (x+4)(x+4) and then you want to get rid of the X from underneath it.

    Think your rules of indices.
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    (Original post by I_Like_Maths)
    For 1a

    Expand the (x+4)(x+4) and then you want to get rid of the X from underneath it.

    Think your rules of indices.
    How do I get 'rid' of x?
    I know that it goes to the power of ^-1 but how do I do that? I'm so confused
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    (Original post by Bevin)
    Hey, I'm really struggling with the harder differentiating questions in C1

    I can do ones such as 5x^3+7x+3 (15x^2+7)

    But the following ones, I really don't understand where to even start

    1) Differentiate with respect to x

    a) (x+4)^2/x

    2) The curve C has the equation y=4x^2 + 5-x/x where x cannot equal 0. The point P on C has x coordinate 1

    a) Show that the value of dy/dx at P is 3
    b)Find an equation of the tangent to C at P

    The tangent meets the x-axis at (k,0)
    c)Find the value of K
    For 1)a) is it (x+4)^{\frac{2}{x}} or \frac{(x+4)^2}{x}? Similarly, with 2) do you mean 4x^2+\frac{5-x}{x} or \frac{4x^2+5-x}{x}?

    Anyhow, for both of them, you should be able to simplify the terms into x^n and use the chain rule to differentiate.

    EDIT: forgot you were doing C1, chain rule isn't needed here, just simplify the powers.
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    (Original post by Bevin)
    How do I get 'rid' of x?
    I know that it goes to the power of ^-1 but how do I do that? I'm so confused
    You should know that x^{-1} is the same as \frac{1}{x}. Therefore dividing by x is the same as multiplying by x^{-1}.
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    (Original post by Malgorithm)
    For 1)a) is it (x+4)^{\frac{2}{x}} or \frac{(x+4)^2}{x}? Similarly, with 2) do you mean 4x^2+\frac{5-x}{x} or \frac{4x^2+5-x}{x}?

    Anyhow, for both of them, you should be able to simplify the terms into x^n and use the chain rule to differentiate.
    For 1a) it is the second option and for 2) it is the first option, sorry for the confusion

    I really don't understand
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    (Original post by Malgorithm)
    You should know that x^{-1} is the same as \frac{1}{x}. Therefore dividing by x is the same as multiplying by x^{-1}.
    Yes, I do know that but where do I put it

    Is it
    x^2+8x+16 all to the power of -1 ?
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    (Original post by Bevin)
    Yes, I do know that but where do I put it

    Is it
    x^2+8x+16 all to the power of -1 ?
    Write each part out separately if it makes it easier to see what to do.

    (x² / x) + (8x / x) + (16 / x)

    Hopefully that makes it easier to see. Assuming you understand what I mean.
    Let me know what you get
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    (Original post by I_Like_Maths)
    Write each part out separately if it makes it easier to see what to do.

    (x² / x) + (8x / x) + (16 / x)

    Hopefully that makes it easier to see. Assuming you understand what I mean.
    Oh I see, Would x^2 divided by x just be x then?
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    (Original post by Bevin)
    Oh I see, Would x^2 divided by x just be x then?
    Correct
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    So for 1a would the answer be -8x^-2 -1

    or am I wrong aha
    (Original post by I_Like_Maths)
    Correct
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    (Original post by Bevin)
    So for 1a would the answer be -8x^-2 -1

    or am I wrong aha
    I didn't get that which makes me think you may not have got it all in the correct form.

    What did you actually differentiate?
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    So for 1a would the answer be -8x^-2 -1

    or am I wrong aha
    (Original post by I_Like_Maths)
    Correct

    (Original post by I_Like_Maths)
    I didn't get that which makes me think you may have got it all in the correct form.

    What did you actually differentiate?
    (x)+(8x^-1)+(16^-1)
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    (Original post by Bevin)
    So for 1a would the answer be -8x^-2 -1

    or am I wrong aha





    (x)+(8x^-1)+(16^-1)
    Careful (8x / x) won't give you (8x^-1)

    And you technically have the last part right just don't forget your x. So (16x^-1)
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    (Original post by I_Like_Maths)
    Careful (8x / x) won't give you (8x^-1)

    And you technically have the last part right just don't forget your x. So (16x^-1)

    erghhh thank you
    so it is
    -16x^-2 + 1?

    I'm so sorry for wasting your time
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    (Original post by Bevin)
    erghhh thank you
    so it is
    -16x^-2 + 1?

    I'm so sorry for wasting your time
    That's what I got.
    Also just take note for if the question says to leave it in it's simplest form.

    (-16x^-2 + 1) Is also (-16/x² + 1)

    It would be harsh for a marker to take marks for this and I think your answer you gave me would be sufficient, but i'd just be cautious of it anyway.

    And don't worry it wasn't time wasted if you understand it better now
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    (Original post by I_Like_Maths)
    That's what I got.
    Also just take note for if the question says to leave it in it's simplest form.

    (-16x^-2 + 1) Is also (-16/x² + 1)

    It would be harsh for a marker to take marks for this and I think your answer you gave me would be sufficient, but i'd just be cautious of it anyway.

    And don't worry it wasn't time wasted if you understand it better now

    Okay thank you so much, I'll have a go at the other questions now

    Thank you!
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    (Original post by Bevin)
    Okay thank you so much, I'll have a go at the other questions now

    Thank you!
    No worries. Was glad to help, Will you be ok with Q2?
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    (Original post by I_Like_Maths)
    No worries. Was glad to help, Will you be ok with Q2?
    Em
    Well
    I managed to differentiate it into 8x-5x^-2
    I subbed x=1
    (obviously this is C1 so I'd have to do this with no calculator)
    I got (8*1)-(5*1^-2)

    If I do 1^-2 multiplied by 5 first, I get 3 but when I do -5^-2 I get 1/25, which isn't the correct answer. So yes, I have done part a

    For part b, I'm assuming I work out the gradient and use y-y1=m(x-x1) but I have no coordinates? agh
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    (Original post by Bevin)
    Em
    Well
    I managed to differentiate it into 8x-5x^-2
    I subbed x=1
    (obviously this is C1 so I'd have to do this with no calculator)
    I got (8*1)-(5*1^-2)

    If I do 1^-2 multiplied by 5 first, I get 3 but when I do -5^-2 I get 1/25, which isn't the correct answer. So yes, I have done part a

    For part b, I'm assuming I work out the gradient and use y-y1=m(x-x1) but I have no coordinates? agh
    Be careful when differentiating with fractions. You have the first term correct, 8x, but the rest of it is not quite right.

    Try splitting up the fraction again like you did in Q1, so you get \frac{5}{x}-\frac{x}{x}.
 
 
 

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