- 4 x ^ { 2 } \cdot ( \frac { 3 } { 8 } x ^ { 3 } ) \cdot ( - 0,5 x ^ { 4 } ) =
Evaluate
\frac{3x^{9}}{4}
Differentiate w.r.t. x
\frac{27x^{8}}{4}
Graph
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-4x^{5}\times \frac{3}{8}\left(-0,5\right)x^{4}
To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.
-4x^{9}\times \frac{3}{8}\left(-0,5\right)
To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.
-\frac{3}{2}x^{9}\left(-0,5\right)
Multiply -4 and \frac{3}{8} to get -\frac{3}{2}.
\frac{3}{4}x^{9}
Multiply -\frac{3}{2} and -0,5 to get \frac{3}{4}.
\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{5}\times \frac{3}{8}\left(-0,5\right)x^{4})
To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.
\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{9}\times \frac{3}{8}\left(-0,5\right))
To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.
\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{3}{2}x^{9}\left(-0,5\right))
Multiply -4 and \frac{3}{8} to get -\frac{3}{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4}x^{9})
Multiply -\frac{3}{2} and -0,5 to get \frac{3}{4}.
9\times \frac{3}{4}x^{9-1}
The derivative of ax^{n} is nax^{n-1}.
\frac{27}{4}x^{9-1}
Multiply 9 times \frac{3}{4}.
\frac{27}{4}x^{8}
Subtract 1 from 9.
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}