Question

Quotient rule

Answer 1

\[g(x) = \frac{ 2e^x+7 }{ 4x^3 }\]

Answer 2

well its u/v

\[u = 2e^x + 7..................... v = 4x^3\]
and
\[u' = 2e^x..........................v' = 12x^2\]

the quotient rule says

\[\frac{dy}{dx} = \frac{v \times u' - u \times v'}{v^2} \]

make the substitutions and simplify

Answer 3

\[\frac{ (4x^3)(2e^2)-(2e^x+7)(12x^2) }{(4x^3)^2 }\]

Answer 4

\[\frac{ 8x^3-24x^2e^x-84x^2 }{ (4x^3)^2 }\]

That's what I got, is that correct?

Answer 5

You'll find a very good explanation of the quotient rule here:
http://1728.org/chainrul.htm

Answer 6

I already know the quotient rule. I just needed help with the simplifying