Differentiate w.r.t. x
-\frac{9}{2x^{\frac{3}{2}}}
Evaluate
65+\frac{9}{\sqrt{x}}
Graph
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-\frac{1}{2}\times 9x^{-\frac{1}{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}.
-\frac{9}{2}x^{-\frac{1}{2}-1}
Multiply -\frac{1}{2} times 9.
-\frac{9}{2}x^{-\frac{3}{2}}
Subtract 1 from -\frac{1}{2}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
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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
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Limits
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