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Differentiating ln functions watch

1. Just refreshing my memory on these.

please check (I think the second one is wrong)

edit: Also

how would you do
2. (Original post by Prokaryotic_crap)
Just refreshing my memory on these.

please check (I think the second one is wrong)
All seem correct to me.
3. All correct!
4. I swear, at some point in my C4 exam, I'm going to put my head in my hands, then scream "I don't know who I am any more"

Thank god I only need a B.
5. (Original post by Prokaryotic_crap)
edit: Also

how would you do
Make a substitution u=5x+1.
6. (Original post by IchiCC)
All seem correct to me.
am I wrong or whenever you differentiate you always get
7. (Original post by Gemini92)
Make a substitution u=5x+1.
oh yeah
8. (Original post by Prokaryotic_crap)
am I wrong or whenever you differentiate you always get
You can rewrite as and differentiate that. lna is a constant so it differentiates to 0 so you're left with the derivative of lnx which is 1/x.
9. (Original post by Prokaryotic_crap)
edit: Also

how would you do

3/5ln(5x+1)

If the differential of the bottom is on the top, then its just ln of the bottom times by whatever constant you need to get it to work.
10. (Original post by Gemini92)
Make a substitution u=5x+1.
Actually, I don't think you'd need to do that substitution.

you'd simply get

I think...
11. (Original post by fibrebiz)
Actually, I don't think you'd need to do that substitution.

you'd simply get

I think...
It'd be 3/5 ln(5x+1)
12. (Original post by Gemini92)
You can rewrite as and differentiate that. lna is a constant so it differentiates to 0 so you're left with the derivitive of lnx which is 1/x.
that makes sense, never thought of that. last night i was differentiating and done and then I noticed I always get 1/x regardless of the coefficient, so I thought I might be doing it wrong
13. (Original post by Prokaryotic_crap)
edit: Also

how would you do
Making a substitution makes it more complicated than it needs to be. Whenever possible, try to do it by inspection.

If you consider , we get

This is close to what we want, but not quite, as we have a 3 in the numerator not a 5, so we can adjust the numerical factor to account for this. If we put a factor of infront to get,

, we get

, hence

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