Question

i need help finding this with quotient rule (3x^4-3x)/(3x^4+3x)

Answer 1

i know the formula just not to good at simplifiying

Answer 2

the fraction can be factorised and then the common term eliminated

\[\frac{3x^4 - 3x}{3x^4 + 3x} = \frac{3x(x^3 -1)}{3x(x^3 +1)} = \frac{x^3 -1}{x^3 +1}\]

Answer 3

then u = x^3 - 1 du/dx = 3x^2
v = 3x+1 dv/dx = 3x^2

Answer 4

im sorry they want us to use quotient rulle for this

Answer 5

to find derivative

Answer 6

yes so you are now using the quotient rule with a simplified algebraic fraction

\[\frac{dy}{dx} =\frac{ (x^3 +1)\times3x^2 - (x^3 - 1)\times 3x^2}{(x^3 +1)^2}\]

this simplifies to

\[\frac{dy}{dx} = \frac{6x^2}{(x^3+1)^2}\]

Answer 7

do the simplifying at the start reduced the amount of simplification at the end...

Answer 8

oh thanks so much