Question

Is it possible to use product rule for the denominator then the quotient rule for the rest of this equation?

Given that y=3x^2+6x-7/(x+1)^2
Show that dy/dx = 20/(x+1)^3

Answer 1

@hartnn

Answer 2

y=(3x^2+6x-7)/(x+1)^2 =(3x^2+6x-7)/(x+1)^(-2)
so, yes you can use product rule now.
but complexity for both product and quotient rule will be almost same...

Answer 3

Sorry I meant to say chain rule seperately for the denominator, then using the quotient rule

Answer 4

chain rule seperately for the denominator <----no
just quotient rule.

Answer 5

So it would be 3x^2+6x-7/(x+1)^2/(2x+2)
I have also tried product rule but can't seem to get the right answer

Answer 6

no no, chain rule won't apply in denominator,
it will apply in nemerator, when you will differentiate (x+2)^2
you know quotient rule, right ?

Answer 7

Yes, when I left it as it is and just used quotient rule I get 6x^3+3x^2+13/(x+1)^4

This is after I have expanded the bracketts

Answer 8

let me try the numerator
(6x+6)(2x+2)^2 - 4(3x^2+6x-7) (2x+2)
= 24 [(x+1)^3] - 8 (3x^3+6x^2-7x+3x^2+6x-7)
= 24 [(x+1)^3] - 8 (3x^3 +9x^2-x-7)
hmm...did i do any mistake anywhere ?

Answer 9

because numerator is not coming 20.....

Answer 10

Not sure this question was for the least amount of marks on the exam but seems to be the most difficult. Also what happened to the your denominator?

Answer 11

in quotient rule Denominator is squared
so, it will remain as (x+1)^4 from beginning

Answer 12

so our numerator must come out to be 20 (x+1)
let me proceed
24 [(x+1)^3] - 8 (3x^3 +9x^2-x-7)
= 24 x^3 + 24*3x^2 +24*3x+24- 24x^3 -24*3x^2 +8x +56
= 24*3x +8x +80
= 80 x+ 80
= 80(x+1)
O.o we are close

Answer 13

ohh... i took, 2x+2 instead of (x+1)
now i am getting 20

Answer 14

(6x+6)(x+1)^2 - 2(3x^2+6x-7) (x+1)
= 6 [(x+1)^3] - 2(3x^3+6x^2-7x+3x^2+6x-7)
= 6 [(x+1)^3] - 2 (3x^3 +9x^2-x-7)
=6 [(x+1)^3] - 2 (3x^3 +9x^2-x-7)
= 6x^3 + 6*3x^2 +6*3x+6- 6x^3 -6*3x^2 +2x +14
=6*3x +2x +20
= 20x+20
= 20(x+1)
it definitely wasn't easy...but just involved lot of algebra

Answer 15

Ah ok so you then cancel out (x+1) from the numerator. Thank you very much, this has helped me a lot

Answer 16

welcome ^_^