Evaluate
4x^{2}+11
Differentiate w.r.t. x
8x
Graph
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11+3x+2x^{2}+9x^{3}-3x+2x^{2}-9x^{3}
Add 7 and 4 to get 11.
11+2x^{2}+9x^{3}+2x^{2}-9x^{3}
Combine 3x and -3x to get 0.
11+4x^{2}+9x^{3}-9x^{3}
Combine 2x^{2} and 2x^{2} to get 4x^{2}.
11+4x^{2}
Combine 9x^{3} and -9x^{3} to get 0.
\frac{\mathrm{d}}{\mathrm{d}x}(11+3x+2x^{2}+9x^{3}-3x+2x^{2}-9x^{3})
Add 7 and 4 to get 11.
\frac{\mathrm{d}}{\mathrm{d}x}(11+2x^{2}+9x^{3}+2x^{2}-9x^{3})
Combine 3x and -3x to get 0.
\frac{\mathrm{d}}{\mathrm{d}x}(11+4x^{2}+9x^{3}-9x^{3})
Combine 2x^{2} and 2x^{2} to get 4x^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(11+4x^{2})
Combine 9x^{3} and -9x^{3} to get 0.
2\times 4x^{2-1}
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}.
8x^{2-1}
Multiply 2 times 4.
8x^{1}
Subtract 1 from 2.
8x
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}