Evaluate
-\frac{x^{2}}{2}
Differentiate w.r.t. x
-x
Graph
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\frac{-\frac{5}{2}x}{5}x
Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.
-\frac{1}{2}xx
Divide -\frac{5}{2}x by 5 to get -\frac{1}{2}x.
-\frac{1}{2}x^{2}
Multiply x and x to get x^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-\frac{5}{2}x}{5}x)
Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.
\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{2}xx)
Divide -\frac{5}{2}x by 5 to get -\frac{1}{2}x.
\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{2}x^{2})
Multiply x and x to get x^{2}.
2\left(-\frac{1}{2}\right)x^{2-1}
The derivative of ax^{n} is nax^{n-1}.
-x^{2-1}
Multiply 2 times -\frac{1}{2}.
-x^{1}
Subtract 1 from 2.
-x
For any term t, t^{1}=t.
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}