Evaluate
3x^{2}+8
Differentiate w.r.t. x
6x
Graph
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3x^{2}+\frac{6x}{x}+2
Combine 2x^{2} and x^{2} to get 3x^{2}.
3x^{2}+6+2
Cancel out x in both numerator and denominator.
3x^{2}+8
Add 6 and 2 to get 8.
\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+\frac{6x}{x}+2)
Combine 2x^{2} and x^{2} to get 3x^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+6+2)
Cancel out x in both numerator and denominator.
\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}+8)
Add 6 and 2 to get 8.
2\times 3x^{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}.
6x^{2-1}
Multiply 2 times 3.
6x^{1}
Subtract 1 from 2.
6x
For any term t, t^{1}=t.
Examples
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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Matrix
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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
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Limits
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