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secondary 4 | E Maths
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Differentiation, can help?
Date Posted: 4 years ago
Views: 330
y = √(x - a)/(b - x) = √(x - a)/√(b - x)
dy/dx = [√(b - x)(1/2√(x - a)) - √(x - a)(-1/2√(b-x) ] / (b - x)
= [½√(b - x)/(x - a) + ½√(x - a)/(b - x) ] / (b - x)
= [√(b - x)/(x - a) + √(x - a)/(b - x) ] / 2(b - x)
When x = (a + b)/2,
dy/dx = [√(b - (a+b)/2)/((a+b)/2 - a) + √( (a+b)/2 - a)/(b - (a+b)/2 ) ] / 2(b - (a+b)/2 )
= [√( (2b - a - b)/2 / (a + b - 2a)/2 ) + √( (a + b -2a)/2 / (2b - a - b)/2 ) ] / (2b - (a + b) )
= [√(b - a)/(b - a) + √(b - a)/(b-a)] / (b - a)
= (√1 + √1) / (b - a)
= 2/(b - a)
dy/dx = [√(b - x)(1/2√(x - a)) - √(x - a)(-1/2√(b-x) ] / (b - x)
= [½√(b - x)/(x - a) + ½√(x - a)/(b - x) ] / (b - x)
= [√(b - x)/(x - a) + √(x - a)/(b - x) ] / 2(b - x)
When x = (a + b)/2,
dy/dx = [√(b - (a+b)/2)/((a+b)/2 - a) + √( (a+b)/2 - a)/(b - (a+b)/2 ) ] / 2(b - (a+b)/2 )
= [√( (2b - a - b)/2 / (a + b - 2a)/2 ) + √( (a + b -2a)/2 / (2b - a - b)/2 ) ] / (2b - (a + b) )
= [√(b - a)/(b - a) + √(b - a)/(b-a)] / (b - a)
= (√1 + √1) / (b - a)
= 2/(b - a)
See 2 Answers
done
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clear
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Dear all, I would like to share my beautiful solution and hopefully dont scare away any innocent kids
Date Posted:
4 years ago
well done
Beautiful indeed. This student had previously submitted a question asking for differentiation of √x from first principles
yes sir true
A level came out x cube first principle derivative， old syllubus 9233 in 2001
Interesting. Looks like it's phased out nowadays. They don't even cover limits now
yes sir，you are right
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