Evaluate
x
Differentiate w.r.t. x
1
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Polynomial
5 problems similar to:
\frac { x } { 3 } + \frac { 2 x } { 5 } + \frac { 4 x } { 15 } =
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\frac{5x}{15}+\frac{3\times 2x}{15}+\frac{4x}{15}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{x}{3} times \frac{5}{5}. Multiply \frac{2x}{5} times \frac{3}{3}.
\frac{5x+3\times 2x}{15}+\frac{4x}{15}
Since \frac{5x}{15} and \frac{3\times 2x}{15} have the same denominator, add them by adding their numerators.
\frac{5x+6x}{15}+\frac{4x}{15}
Do the multiplications in 5x+3\times 2x.
\frac{11x}{15}+\frac{4x}{15}
Combine like terms in 5x+6x.
\frac{11x+4x}{15}
Since \frac{11x}{15} and \frac{4x}{15} have the same denominator, add them by adding their numerators.
\frac{15x}{15}
Combine like terms in 11x+4x.
x
Cancel out 15 and 15.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{15}+\frac{3\times 2x}{15}+\frac{4x}{15})
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 5 is 15. Multiply \frac{x}{3} times \frac{5}{5}. Multiply \frac{2x}{5} times \frac{3}{3}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x+3\times 2x}{15}+\frac{4x}{15})
Since \frac{5x}{15} and \frac{3\times 2x}{15} have the same denominator, add them by adding their numerators.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x+6x}{15}+\frac{4x}{15})
Do the multiplications in 5x+3\times 2x.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x}{15}+\frac{4x}{15})
Combine like terms in 5x+6x.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+4x}{15})
Since \frac{11x}{15} and \frac{4x}{15} have the same denominator, add them by adding their numerators.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15x}{15})
Combine like terms in 11x+4x.
\frac{\mathrm{d}}{\mathrm{d}x}(x)
Cancel out 15 and 15.
x^{1-1}
The derivative of ax^{n} is nax^{n-1}.
x^{0}
Subtract 1 from 1.
1
For any term t except 0, t^{0}=1.
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}