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Differentiate

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.
Reply 2
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
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)2x(x+4)^{\frac{2}{x}} or (x+4)2x\frac{(x+4)^2}{x}? Similarly, with 2) do you mean 4x2+5xx4x^2+\frac{5-x}{x} or 4x2+5xx\frac{4x^2+5-x}{x}?

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

EDIT: forgot you were doing C1, chain rule isn't needed here, just simplify the powers.
(edited 9 years ago)
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 x1x^{-1} is the same as 1x\frac{1}{x}. Therefore dividing by xx is the same as multiplying by x1x^{-1}.
Reply 5
Original post by Malgorithm
For 1)a) is it (x+4)2x(x+4)^{\frac{2}{x}} or (x+4)2x\frac{(x+4)^2}{x}? Similarly, with 2) do you mean 4x2+5xx4x^2+\frac{5-x}{x} or 4x2+5xx\frac{4x^2+5-x}{x}?

Anyhow, for both of them, you should be able to simplify the terms into xnx^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
Reply 6
Original post by Malgorithm
You should know that x1x^{-1} is the same as 1x\frac{1}{x}. Therefore dividing by xx is the same as multiplying by x1x^{-1}.


Yes, I do know that but where do I put it

Is it
x^2+8x+16 all to the power of -1 ?
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:smile:
(edited 9 years ago)
Reply 8
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?
Original post by Bevin
Oh I see, Would x^2 divided by x just be x then?


Correct:smile:
Reply 10
So for 1a would the answer be -8x^-2 -1

or am I wrong aha
Original post by I_Like_Maths
Correct:smile:
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?:smile:
Reply 12
So for 1a would the answer be -8x^-2 -1

or am I wrong aha
Original post by I_Like_Maths
Correct:smile:



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?:smile:


(x)+(8x^-1)+(16^-1)
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)
Reply 14
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
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.:biggrin:
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:smile:
(edited 9 years ago)
Reply 16
Original post by I_Like_Maths
That's what I got.:biggrin:
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:smile:



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

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

Thank you!


No worries. Was glad to help, Will you be ok with Q2?
Reply 18
Original post by I_Like_Maths
No worries. Was glad to help, Will you be ok with Q2?


Em
Well :biggrin:
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
Original post by Bevin
Em
Well :biggrin:
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, 8x8x, but the rest of it is not quite right.

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

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