f ( x ) = - \frac { 3 } { 2 } ( 3 x ^ { 3 } - 3 x
Solve for f (complex solution)
\left\{\begin{matrix}\\f=\frac{9-9x^{2}}{2}\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}\\f=\frac{9-9x^{2}}{2}\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x (complex solution)
x=\frac{\sqrt{9-2f}}{3}
x=0
x=-\frac{\sqrt{9-2f}}{3}
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{\sqrt{9-2f}}{3}\text{; }x=-\frac{\sqrt{9-2f}}{3}\text{, }&f\leq \frac{9}{2}\end{matrix}\right.
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fx=-\frac{9}{2}x^{3}+\frac{9}{2}x
Use the distributive property to multiply -\frac{3}{2} by 3x^{3}-3x.
xf=\frac{9x-9x^{3}}{2}
The equation is in standard form.
\frac{xf}{x}=\frac{9x-9x^{3}}{2x}
Divide both sides by x.
f=\frac{9x-9x^{3}}{2x}
Dividing by x undoes the multiplication by x.
f=\frac{9-9x^{2}}{2}
Divide \frac{-9x^{3}+9x}{2} by x.
fx=-\frac{9}{2}x^{3}+\frac{9}{2}x
Use the distributive property to multiply -\frac{3}{2} by 3x^{3}-3x.
xf=\frac{9x-9x^{3}}{2}
The equation is in standard form.
\frac{xf}{x}=\frac{9x-9x^{3}}{2x}
Divide both sides by x.
f=\frac{9x-9x^{3}}{2x}
Dividing by x undoes the multiplication by x.
f=\frac{9-9x^{2}}{2}
Divide \frac{-9x^{3}+9x}{2} by x.
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}