f ^ { \prime } ( x ) = x ^ { 2 } d x
Solve for d (complex solution)
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for d
\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for f (complex solution)
f\in \mathrm{C}
d=0\text{ or }x=0
Solve for f
f\in \mathrm{R}
d=0\text{ or }x=0
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\frac{\mathrm{d}}{\mathrm{d}x}(f)x=x^{3}d
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
x^{3}d=\frac{\mathrm{d}}{\mathrm{d}x}(f)x
Swap sides so that all variable terms are on the left hand side.
x^{3}d=0
The equation is in standard form.
d=0
Divide 0 by x^{3}.
\frac{\mathrm{d}}{\mathrm{d}x}(f)x=x^{3}d
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
x^{3}d=\frac{\mathrm{d}}{\mathrm{d}x}(f)x
Swap sides so that all variable terms are on the left hand side.
x^{3}d=0
The equation is in standard form.
d=0
Divide 0 by x^{3}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}