SOLUTION: i need the derivative of
{{{ (2x^2-10)/(x^2+5)^2 }}}
i came up with a final answer of
{{{ 4x*(-x^4+10x^2+75)/(x^2+5)^4 }}}
but those numbers seem too weird for that to
Algebra.Com
Question 248534: i need the derivative of
i came up with a final answer of
but those numbers seem too weird for that to be the correct answer.. please help.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Everything is right except for one sign in the numerator:
\ =\ \frac{g^{\prime}(x)h(x)\ -\ g(x)h^{\prime}(x)}{\left[h(x)\right]^2})
\ =\ 2x^2\ -\ 10)
\ =\ 4x)
\ =\ \left(x^2\ +\ 5\right)^2)
We need the chain rule for this one:
Let 
, so 
and 
, hence:
\ =\ 4x^3\ +\ 20x)
Putting it all together:
^2\ -\ \left(2x^2\ -\ 10\right)\left(4x^3\ +\ 20x\right)}{\left[x^2\ +\ 5\right]^4})
\ -\ \left(8x^5\ +\ 40x^3\ -\ 40x^3\ -\ 200x\right)}{\left[x^2\ +\ 5\right]^4})
}{\left[x^2\ +\ 5\right]^4})
Though I might have written it thus:
}{\left[x^2\ +\ 5\right]^4})
But that is just changing 'happy' to 'glad' actually.
John
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