Evaluate
\left(x+1\right)\left(3x+1\right)
Differentiate w.r.t. x
6x+4
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\frac{\mathrm{d}}{\mathrm{d}x}(x\left(1+2x+x^{2}\right))
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+x\right)^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(x+2x^{2}+x^{3})
Use the distributive property to multiply x by 1+2x+x^{2}.
x^{1-1}+2\times 2x^{2-1}+3x^{3-1}
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.
x^{0}+2\times 2x^{2-1}+3x^{3-1}
Subtract 1 from 1.
x^{0}+4x^{2-1}+3x^{3-1}
Multiply 2 times 2.
x^{0}+4x^{1}+3x^{3-1}
Subtract 1 from 2.
x^{0}+4x^{1}+3x^{2}
Subtract 1 from 3.
x^{0}+4x+3x^{2}
For any term t, t^{1}=t.
1+4x+3x^{2}
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}