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Formula
Calculate the differentiation
Solve the equation
Graph
$y = \dfrac { 3 } { x ^ { 3 } } + x ^ { - 4 }$
$x$Intercept
$\left ( - \dfrac { 1 } { 3 } , 0 \right )$
$y = \dfrac{ 3 }{ x ^{ 3 } } +x ^{ -4 }$
$\dfrac {d } {d x } {\left( y \right)} = - \dfrac { 9 x + 4 } { x ^ { 5 } }$
Calculate the differentiation of the logarithmic function
$\dfrac {d } {d \color{#FF6800}{ x } } {\left( \color{#FF6800}{ \dfrac { 3 } { x ^ { 3 } } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } } \right)}$
 Calculate the differentiation 
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 9 x + 4 } { x ^ { 5 } } }$
$\begin{cases} 3 x + 1 = x ^ { 4 } y \\ x \neq 0 \end{cases}$
Solve the fractional equation
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 3 } { x ^ { 3 } } } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Simplify the expression 
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 3 x + 1 } { x ^ { 4 } } }$
$\color{#FF6800}{ y } = \color{#FF6800}{ \dfrac { 3 x + 1 } { x ^ { 4 } } }$
 Reverse the left and right terms of the equation (or inequality) 
$\color{#FF6800}{ \dfrac { 3 x + 1 } { x ^ { 4 } } } = \color{#FF6800}{ y }$
$\color{#FF6800}{ \dfrac { 3 x + 1 } { x ^ { 4 } } } = \color{#FF6800}{ y }$
 If $\frac{a(x)}{b(x)} = c(x)$ is valid, it is $\begin{cases} a(x) = b(x) c(x) \\ b(x) \ne 0 \end{cases}$
$\begin{cases} \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } = \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ y } \\ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \neq \color{#FF6800}{ 0 } \end{cases}$
$\begin{cases} 3 x + 1 = x ^ { 4 } y \\ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } \neq \color{#FF6800}{ 0 } \end{cases}$
 If $f(x)^{n} \ne 0$ is valid, it is $f(x) \ne 0$
$\begin{cases} 3 x + 1 = x ^ { 4 } y \\ \color{#FF6800}{ x } \neq \color{#FF6800}{ 0 } \end{cases}$
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