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May
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accepted Calculating permutations if the sequences have to be in ascending order?
May
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awarded  Supporter
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asked Calculating permutations if the sequences have to be in ascending order?
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comment In integration notation - why can you multiply du by a number?
Say then you have the function $f(x) = x^{2}$ for which $f'(x) = 2x$. So the equation of the tangent at $x = 1 e.g. f'(1)$ is 2 but how does that relate to $dy = f'(1)dx$? Oh I think I see it now $dy = 2 dx$ is a function just like $y=mx+c$ which you can manipulate? Is that correct?
May
2
comment In integration notation - why can you multiply du by a number?
So the derivative $f'(x)$ is a function that describes the gradient of a function $f(x)$ but for a given point $a$ it is also the equation/function of a tangent - I'm assuming thats roughly what is meant by linear approximation. But this tangent $f'(a)$ also takes a variable $dx$ which makes it describe $dy$, how does that work?
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awarded  Scholar
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comment In integration notation - why can you multiply du by a number?
Makes sense, thanks!
May
2
accepted In integration notation - why can you multiply du by a number?
May
2
comment In integration notation - why can you multiply du by a number?
Out of interest because I haven't come across it yet, where else is $dx$ written on its own?
May
2
comment In integration notation - why can you multiply du by a number?
I think I understand, du & dx are 'made up' for want of a better term quantities that we use to manipulate. So $\int \sin(u)$ $2du$ is actually ($\int \sin(u)) * (2) * (du)? $ or rather $(\int \sin(u) du) * 2$
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awarded  Analytical
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awarded  Student
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asked In integration notation - why can you multiply du by a number?