f ( x ) = \frac { 1 } { x ^ { 2 } } d x
Solve for d
d=fx^{2}
x\neq 0
Solve for f
f=\frac{d}{x^{2}}
x\neq 0
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fxx^{2}=1dx
Multiply both sides of the equation by x^{2}.
fx^{3}=1dx
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
1dx=fx^{3}
Swap sides so that all variable terms are on the left hand side.
dx=fx^{3}
Reorder the terms.
xd=fx^{3}
The equation is in standard form.
\frac{xd}{x}=\frac{fx^{3}}{x}
Divide both sides by x.
d=\frac{fx^{3}}{x}
Dividing by x undoes the multiplication by x.
d=fx^{2}
Divide fx^{3} by x.
fxx^{2}=1dx
Multiply both sides of the equation by x^{2}.
fx^{3}=1dx
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
fx^{3}=dx
Reorder the terms.
x^{3}f=dx
The equation is in standard form.
\frac{x^{3}f}{x^{3}}=\frac{dx}{x^{3}}
Divide both sides by x^{3}.
f=\frac{dx}{x^{3}}
Dividing by x^{3} undoes the multiplication by x^{3}.
f=\frac{d}{x^{2}}
Divide dx by x^{3}.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
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}