![\displaystyle \frac{d}{dx} \Big [ \frac{3}{x^2} \Big ]=-\frac{6}{x^3}](/tpl/images/1018/5970/b98d9.png)
![\displaystyle \frac{d}{dx}[ x^n] = nx^n^-^1](/tpl/images/1018/5970/22c04.png)
as 
which is equivalent to 
.
. ![\displaystyle \frac{d}{dx} \Big [ \frac{f(x)}{g(x)} \Big ]=\frac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}](/tpl/images/1018/5970/3c06e.png)
![\displaystyle \frac{d}{d x}\left[\frac{3}{x^2}\right] = -\frac{6}{x^{3}}](/tpl/images/1018/5970/0bafd.png)
. 
and 
denote two functions of 
. Assume that 
. The quotient rule states that:![\displaystyle \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right] = \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2}](/tpl/images/1018/5970/f2ce9.png)
.
(a constant function.)The denominator of the fraction is 
.
and 
.
regardless of the value of 
.
represents a rational number (such as 
,) then by the power rule, ![\displaystyle \frac{d}{d x}\left[{x}^{m}\right] = m\, {x}^{m-1}](/tpl/images/1018/5970/f897f.png)
.![\begin{aligned}{g}^{\prime}(x) &= \frac{d}{d x} \left[x^{2}\right] \\ &= 2\, x^{2 - 1} \\ &= 2\, x\end{aligned}](/tpl/images/1018/5970/12ca6.png)
.
into the quotient rule expression to find ![\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right]](/tpl/images/1018/5970/00269.png)
:![\begin{aligned}&\; \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] \quad \genfrac{}{}{0em}{}{\leftarrow f(x) = 3}{\leftarrow g(x) = {x}^{2}} \\ =&\; \frac{d}{d x}\left[\frac{f(x)}{g(x)}\right]\\ =&\; \frac{{f}^\prime(x) \cdot g(x) - f(x) \cdot g^{\prime}(x)}{{(g(x))}^2} \\ =& \; \frac{0 \, x^2 - 3\, (2\, x)}{\left({x}^{2}\right)} \\ =&\; -\frac{6}{x^{3}}\end{aligned}](/tpl/images/1018/5970/7f56d.png)
.![\displaystyle \frac{d}{d x}\left[\frac{3}{{x}^{2}}\right] = -\frac{6}{x^{3}}](/tpl/images/1018/5970/23d1d.png)
.
Use the quotient rule to find the derrivatives of 3/x^2
With full process...
Mathematics, 07.01.2021 14:00, Gogontle8347
Use the quotient rule to find the derrivatives of 3/x^2
With full process
Answers: 3
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