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# Further Calculus - Differentiation (Chain Rule) watch

1. Hi all,

I'm doing higher maths (Scottish curriculum), have my prelim tomorrow, and despite having studied for about 2 weeks and doing all the past papers in my book, I'm still completely unable to do certain questions. For example, from a past prelim paper:

A function, f, is defined on a suitable domain as
(a) Differentiate f with respect to x, expressing your answer with positive indices.
(b) Find the equation of the tangent to the curve y=f(x) at 0.
I THINK part a is done by bringing the bracket up to the top, making the power -3 and using the chain rule, which I'm fine doing, but the main issue is the 3 outside the bracket, I really don't know what to do with it! This paper actually has solutions but I can't make sense of them. It's saying something about differentiating power, differentiating inside, which I think is just the chain rule but I learned it by y=u to the power whatever, u=the bracket, differentiate them separately, multiply the answers and sub in the u value. Can anyone offer any advice?
T'would be much appreciated, thankies!
x
2. just leave the 1/3rd out of it

and differentiate (1-x)^-3 then multiply it by the 1/3rd when you're done
3. Ahaa thank you! That was really obvious, I was just getting myself confused by the 3. When I do it the way you said I get the right answer (apparently ) without multiplying by the third. When I do, obviously I get the wrong answer! It's likely something to do with a silly mistake or dodgy algebra somewhere though, I'll have a double and triple check through my working and hopefully figure it out. Thank you
4. (Original post by MySweetheartTheDrunk)
Ahaa thank you! That was really obvious, I was just getting myself confused by the 3. When I do it the way you said I get the right answer (apparently ) without multiplying by the third. When I do, obviously I get the wrong answer! It's likely something to do with a silly mistake or dodgy algebra somewhere though, I'll have a double and triple check through my working and hopefully figure it out. Thank you
Don't you need the 1/3 to cancel out with the 3 generated by differentiation of U to the power of -3 (where ). This is . So the third and the 3 multiply to 1?

So you get stuck with a minus sign. But . So the two minuses give a positive result?
5. (Original post by MySweetheartTheDrunk)
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