Question

Use the quotient rule to find the derivative.
y=2x^2+3x/x^3+6

Answer 1

The derivative is:
\[-\frac{ 6 }{ x^3 }+4x\]Hope this helps, give me a medal if it does!

Answer 2

how did u get that

Answer 3

quotient rule

Answer 4

can u show me a step by step im lost

Answer 5

Is ur question? @mizzgivens1
\[y=\frac{ 2x^2+3x }{ x^3+6 }\]

Answer 6

yes y=2x^2+3x / x^3+6
i dont know how to get the answer step by step

Answer 7

you know the quotient rule?

Answer 8

g(x)*f'(x)-f(x)-g'(x) / (g(x))^2

Answer 9

\[f ' x/= ((4x+3).(x³+6)-(2x²+3x).(3x²))/((x³+6)²)\]

Answer 10

\[\left(\begin{matrix}f(x) \\ g(x)\end{matrix}\right)'=\frac{ f'(x)*g(x)-g'(x)*f(x) }{ ( g(x) )^2 }\]

Answer 11

how do you get f '(x) and g '(x)

Answer 12

f(x)=2x^2+3x
the derivative of 2x^2 = 4x
this because the derivative of x^n = nx^n-1
there is a 2 before the x, you multiply that one with the exponent, thats 2 in this case
then n-1, 2-1 = 1. something to the power 1 is just the same so the 1 is not written.

The derivative of 3x = x because the unwritten exponent is 1. you multiply that with the number before x, this is 3. 3*1 = 3. then you do the exponent -1, this will be 0. something to the power 0 = 0 so the x falls away

f'(x)= 4x+3

Answer 13

you do the same thing for g(x)

Answer 14

i got stuck. for x^3+6, i got 3x^2 but what happens to the +6 how do i put that into the equation nx^n-1?

Answer 15

is it because there is no exponent so it cancels the 6 out?

Answer 16

the derivative of x^3 is 3x^2.
There is a rule: a' = 0, a being a constant like 6

Answer 17

so yes the 6 is canceled out

Answer 18

Now that you know f'(x) and g'(x), you can fill them in the quotient rule.

Answer 19

so far i have 4x^4+3x^3+24x+18-6x^4+9x^3 / (x^3+6)^2

Answer 20

\[y=\frac{ 2x^2+3x }{ x^3+6}\]
\[\left(\frac{ f(x) }{ g(x) }\right)'=\frac{ f'(x)*g(x)-g'(x)*f(x) }{ (g(x))^2 }\rightarrow \frac{ (4x+3)*(x^3+6)-(2x^2+3x)*(3x^2) }{ (x^3+6)(x^3+6)}\]

Answer 21

You can cancel 1 of the (x^3+6) out because they're both in the numerator and denominator\[ \frac{ (4x+3)-(2x^2+3x)*(3x^2) }{ (x^3+6)} \]

Answer 22

@mizzgivens1 you solved it?

Answer 23

yes i got it thanx for the help