Evaluate
6x^{2}+5x+3
Differentiate w.r.t. x
12x+5
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6x^{2}+5x+3+0
Multiply -1 and 0 to get 0.
6x^{2}+5x+3
Add 3 and 0 to get 3.
2\times 6x^{2-1}+5x^{1-1}
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}.
12x^{2-1}+5x^{1-1}
Multiply 2 times 6.
12x^{1}+5x^{1-1}
Subtract 1 from 2.
12x^{1}+5x^{0}
Subtract 1 from 1.
12x+5x^{0}
For any term t, t^{1}=t.
12x+5\times 1
For any term t except 0, t^{0}=1.
12x+5
For any term t, t\times 1=t and 1t=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}