got some variables in an example that are being combined, as follows:
2x * x^2 + 4 - x^2 * 2x = 8x
does this really equal 8x?
(2x*x^2) + 4 -(x^2*2x)
both left and right cancel out leaving the 4 no?
i'm sure i'm missing something simple.
got some variables in an example that are being combined, as follows:
2x * x^2 + 4 - x^2 * 2x = 8x
does this really equal 8x?
(2x*x^2) + 4 -(x^2*2x)
both left and right cancel out leaving the 4 no?
i'm sure i'm missing something simple.
Ok, so, you will need to use the quotient rule, which is if
$\displaystyle y = \frac{u}{v}$, then $\displaystyle y' = \frac{v \frac{du}{dv} - u\frac{dv}{du}}{v^2$
This gives:
$\displaystyle \frac{d(\frac{x^2}{x^2 + 4})}{dx} = \frac{(x^2 + 4).2x - x^2(2x)}{(x^2 +4)^2}$
$\displaystyle = \frac{2x^3 + 8x - 2x^3}{x^4 + 8x^2 + 16}$
Now, you get 8x.
Ok, so, you will need to use the quotient rule, which is if
$\displaystyle y = \frac{u}{v}$, then $\displaystyle y' = \frac{v \frac{du}{dv} - u\frac{dv}{du}}{v^2}$
This gives:
$\displaystyle \frac{d(\frac{x^2}{x^2 + 4})}{dx} = \frac{(x^2 + 4).2x - x^2(2x)}{(x^2 +4)^2}$
$\displaystyle = \frac{2x^3 + 8x - 2x^3}{x^4 + 8x^2 + 16}$
Now, you get 8x.