J's answer to huihuibuhui's Secondary 3 A Maths Singapore question.
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
x/(1 + x)
= (x + 1 - 1)/(1 + x)
= (x + 1)/(1 + x) - 1/(1 + x)
= 1 - 1/(1 + x)
So x/(1 + x) ≡ 1 - 1/(1 + x)
(≡ stands for 'equivalent to' or 'identical to' , in geometry it is 'congruent to' .
It is also used in modular arithmetic eg. 15 ≡ 3 mod 4 )
So, d/dx x/(1 + x)
= d/dx (1 - 1/(1 + x))
= d/dx (1 - (1 + x)-¹)
= 0 - (-1)(1 + x)-²
= 1/(1 + x)²
= (x + 1 - 1)/(1 + x)
= (x + 1)/(1 + x) - 1/(1 + x)
= 1 - 1/(1 + x)
So x/(1 + x) ≡ 1 - 1/(1 + x)
(≡ stands for 'equivalent to' or 'identical to' , in geometry it is 'congruent to' .
It is also used in modular arithmetic eg. 15 ≡ 3 mod 4 )
So, d/dx x/(1 + x)
= d/dx (1 - 1/(1 + x))
= d/dx (1 - (1 + x)-¹)
= 0 - (-1)(1 + x)-²
= 1/(1 + x)²
Date Posted:
3 years ago
Thank you so much:)
Thank you so much
360 Tutoring Program