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# C4 Differentiation - 2 questions Watch

1. Okay, the book says that if . Then, in one of the questions I need to differentiate . So I use the general rule above and get , however they got . Am I missing something here?

Second question:

The book explains how to differentiate the general power function:

Ok.. stopping there, surely that's not correct? They differentiated lny, and by using the chain rule got . Then, by definition, shouldn't you get for the RHS? How did they just get lna?
2. (Original post by ViralRiver)
Okay, the book says that if . Then, in one of the questions I need to differentiate . So I use the general rule above and get , however they got . Am I missing something here?
The book is wrong and so are you.
Note that . Apply your rule to this and you will get .

Second question:

The book explains how to differentiate the general power function:

Ok.. stopping there, surely that's not correct? They differentiated lny, and by using the chain rule got . Then, by definition, shouldn't you get for the RHS? How did they just get lna?
That's correct. When you differentiate w.r.t. x, you get . is of this form.
3. I'm guessing you mean . Remember to use the chain rule.

As for the second part, a is a constant, so its derivative is 0.
4. (Original post by Farhan.Hanif93)
The book is wrong and so are you.
Note that . Apply your rule to this and you will get .

That's correct. When you differentiate w.r.t. x, you get . is of this form.
SOrry, I meant the book got -2^-xln2, which is what I don't understand. What do you mean by your response to the second question?
5. similarly, what's ?
6. (Original post by Pheylan)
similarly, what's ?
7. (Original post by ViralRiver)
SOrry, I meant the book got -2^-xln2, which is what I don't understand.

What do you mean by your response to the second question?
a is not a variable, it's a constant. Therefore lna is a constant. When you differentiate for some constant coefficient, n, you get the derivative to be , right? C1 differentiation?
So .
8. (Original post by Pork and Beans)
I'm guessing you mean . Remember to use the chain rule.

As for the second part, a is a constant, so its derivative is 0.
Well, how do we know a is a constant? I'm still unsure of how to get -2 etc for the first part, even with the chain rule >< - this doesn't seem to make any sense.
9. (Original post by Farhan.Hanif93)

a is not a variable, it's a constant. Therefore lna is a constant. When you differentiate for some constant coefficient, n, you get the derivative to be , right? C1 differentiation?
So .
Okay, I understand it a bit more now, but I still have a few problems. If then , which doesn't make a difference in this question, but why did you raise the entire fraction (1/2) to the power of x?
10. (Original post by ViralRiver)
Okay, I understand it a bit more now, but I still have a few problems. If then , which doesn't make a difference in this question, but why did you raise the entire fraction (1/2) to the power of x?
To apply the rule you stated. You can always do it the long way. To be in the form , which you want, you need the coefficient of x in the power to be 1. It's still equivalent because .
11. (Original post by Farhan.Hanif93)
To apply the rule you stated. You can always do it the long way. To be in the form , which you want, you need the coefficient of x in the power to be 1. It's still equivalent because .
Perfect, thanks .

Is there a sort of general rule in a similar way to the following:?

12. (Original post by ViralRiver)
Perfect, thanks .

Is there a sort of general rule in a similar way to the following:?

Yes, that is true.
13. (Original post by Farhan.Hanif93)
Yes, that is true.
Hmm, soryr I should be more clear.

I can use the chain rule to differentiate sin, as follows:

then, if

but.. what if , how do you use the chain rule on that?

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Updated: December 9, 2010
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