Solve for f (complex solution)
\left\{\begin{matrix}\\f=\frac{1}{2e^{x}}\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}\\f=\frac{1}{2e^{x}}\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\left(\ln(f)+\ln(2)\right)+2\pi n_{1}i\text{, }n_{1}\in \mathrm{Z}\text{, }&f\neq 0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\left(\ln(f)+\ln(2)\right)\text{, }&f>0\end{matrix}\right.
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2xf=\frac{x}{e^{x}}
The equation is in standard form.
\frac{2xf}{2x}=\frac{x}{e^{x}\times 2x}
Divide both sides by 2x.
f=\frac{x}{e^{x}\times 2x}
Dividing by 2x undoes the multiplication by 2x.
f=\frac{1}{2e^{x}}
Divide \frac{x}{e^{x}} by 2x.
2xf=\frac{x}{e^{x}}
The equation is in standard form.
\frac{2xf}{2x}=\frac{x}{e^{x}\times 2x}
Divide both sides by 2x.
f=\frac{x}{e^{x}\times 2x}
Dividing by 2x undoes the multiplication by 2x.
f=\frac{1}{2e^{x}}
Divide \frac{x}{e^{x}} by 2x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Matrix
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Simultaneous equation
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Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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