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Core 3 Differentiation

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1. Hi,
I know this is probably an easy question but how would you go about differentiating 4ln2x? Thanks
2. (Original post by student1856)
Hi,
I know this is probably an easy question but how would you go about differentiating 4ln2x? Thanks
Use the Chain rule.
3. (Original post by zetamcfc)
Use the Chain rule.
What part of it would I set as U? Would it be y=4U with U equalling ln2x?
4. (Original post by student1856)
What part of it would I set as U? Would it be y=4U with U equalling ln2x?
u=2x.
5. (Original post by student1856)
Hi,
I know this is probably an easy question but how would you go about differentiating 4ln2x? Thanks

6. 4 is a constant,
dy/dx(Inx) would be 1/x

as for ln2x:

dy/dx(In2x) = dy/dx(Inu) = 2/u = 2/2x = 1/x

so, dy/dx = constant/x.
7. (Original post by zetamcfc)
u=2x.
Right, so I do that and I get 2 multiplied by 4/x which gives me 8/x. But the answer is 4/x.
8. (Original post by student1856)
Right, so I do that and I get 2 multiplied by 4/x which gives me 8/x. But the answer is 4/x.
9. (Original post by student1856)
Right, so I do that and I get 2 multiplied by 4/x which gives me 8/x. But the answer is 4/x.
y=4lnu implies dy/dx = 4/u * du/dx
10. (Original post by XOR_)
4 is a constant,
dy/dx(Inx) would be 1/x

as for ln2x:

dy/dx(In2x) = dy/dx(Inu) = 2/u = 2/2x = 1/x

so, dy/dx = constant/x.

So, why is 4 a constant here but when you calculate 4lnx, 4 is not a constant? Why do you include the 4 in the diffeentiationof 4lnx but not in 4ln2x? Thank you
11. (Original post by student1856)
So, why is 4 a constant here but when you calculate 4lnx, 4 is not a constant? Why do you include the 4 in the diffeentiationof 4lnx but not in 4ln2x? Thank you
dy/dx(4lnx) = 4/x

dy/dx(4ln2x) = 4/x

for dy/dx(ln2x),
when u = 2x, you get dy/dx(lnu) = 2/2x = 1/x.
12. (Original post by student1856)
So, why is 4 a constant here but when you calculate 4lnx, 4 is not a constant? Why do you include the 4 in the diffeentiationof 4lnx but not in 4ln2x? Thank you
Would it help if we did this:

.

So:
13. (Original post by XOR_)
dy/dx(4lnx) = 4/x

dy/dx(4ln2x) = 4/x

for dy/dx(ln2x),
when u = 2x, you get dy/dx(lnu) = 2/2x = 1/x.
Ahh, I get it now. Thank you very much
14. (Original post by Zacken)
Would it help if we did this:

.

So:
Yes it does, thanks Zacken
15. (Original post by student1856)
Yes it does, thanks Zacken

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