Differentiate w.r.t. x
\frac{3\sqrt{x}}{4}
Evaluate
\frac{x^{\frac{3}{2}}}{2}
Graph
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\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{2\sqrt{x}})
Factor the expressions that are not already factored in \frac{x^{2}}{2\sqrt{x}}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{\frac{3}{2}}}{2})
Cancel out \sqrt{x} in both numerator and denominator.
\frac{3}{2}\times \frac{1}{2}x^{\frac{3}{2}-1}
The derivative of ax^{n} is nax^{n-1}.
\frac{3}{4}x^{\frac{3}{2}-1}
Multiply \frac{3}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.
\frac{3}{4}\sqrt{x}
Subtract 1 from \frac{3}{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}