c3 differentiation help

quotient rule
differentiate
3x^2/(2x-1)^2
i have got it to the form of the quotient rule

(2x-1)^2(6x) - 3x^2 (4(2x-1) /(2x-1)^4
now what

Reply 1

jhpy1024

{ 6x(2x-1)^2 - 12(2x-1)x^2 } / (2x-1)^4

= { 6x(2x-1)[(2x-1)-2x] } / (2x-1)^4

You won't need to simplify further.

Reply 2

coolgamer

Original post by Arithmeticae

tbh i wouldn't use the quotient rule here, the product rule with

3x^2 (2x-1)^{-2}

is easier imo

but its a rational function

Reply 3

coolgamer

Original post by jhpy1024

{ 6x(2x-1)^2 - 12(2x-1)x^2 } / (2x-1)^4

= { 6x(2x-1)[(2x-1)-2x] } / (2x-1)^4

You won't need to simplify further.

but answer is
− 6x / ( 2x − 1 ) 3

Reply 4

jhpy1024

Original post by coolgamer

but answer is
− 6x / ( 2x − 1 ) 3

Ah okay, so you need to simplify to get all the marks? In that case, start by expanding the brackets in the numerator.

Reply 5

MathsNerd1

Original post by coolgamer

quotient rule
differentiate
3x^2/(2x-1)^2
i have got it to the form of the quotient rule

(2x-1)^2(6x) - 3x^2 (4(2x-1) /(2x-1)^4
now what

Moved to Maths section :smile:

Reply 6

coolgamer

Original post by jhpy1024

Ah okay, so you need to simplify to get all the marks? In that case, start by expanding the brackets in the numerator.

for the numerator i got 12x^2-6x-24x^3+3x2 which i think is wrong :/

Reply 7

jhpy1024

Original post by coolgamer

for the numerator i got 12x^2-6x-24x^3+3x2 which i think is wrong :/

Here ya go :smile:

http://mathb.in/23847

Reply 8

TenOfThem

Original post by coolgamer

quotient rule
differentiate
3x^2/(2x-1)^2
i have got it to the form of the quotient rule

(2x-1)^2(6x) - 3x^2 (4(2x-1) /(2x-1)^4
now what

Well first,learn how to use LaTeX

\dfrac{6x(2x-1)^2-(3x^2)4(2x-1)}{(2x-1)^4}

\dfrac{(2x-1)(12x^2-6x-12x^2)}{(2x-1)^4}

Cancels easily to the required answer

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c3 differentiation help

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