Evaluate
3x_{3}^{5}
Differentiate w.r.t. x_3
15x_{3}^{4}
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3^{1}x_{3}^{1}x_{3}^{1}x_{3}^{1}x_{3}^{1}x_{3}^{1}
Use the rules of exponents to simplify the expression.
3^{1}x_{3}^{1}x_{3}^{1+1}x_{3}^{1+1}
To multiply powers of the same base, add their exponents.
3^{1}x_{3}^{1}x_{3}^{2}x_{3}^{1+1}
Add the exponents 1 and 1.
3^{1}x_{3}^{1}x_{3}^{2}x_{3}^{2}
Add the exponents 1 and 1.
3x_{3}x_{3}^{2}x_{3}^{2}
Multiply 3 times x_{3}.
\frac{\mathrm{d}}{\mathrm{d}x_{3}}(3x_{3}^{2}x_{3}x_{3}x_{3})
Multiply x_{3} and x_{3} to get x_{3}^{2}.
\frac{\mathrm{d}}{\mathrm{d}x_{3}}(3x_{3}^{3}x_{3}x_{3})
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
\frac{\mathrm{d}}{\mathrm{d}x_{3}}(3x_{3}^{4}x_{3})
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
\frac{\mathrm{d}}{\mathrm{d}x_{3}}(3x_{3}^{5})
To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.
5\times 3x_{3}^{5-1}
The derivative of ax^{n} is nax^{n-1}.
15x_{3}^{5-1}
Multiply 5 times 3.
15x_{3}^{4}
Subtract 1 from 5.
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}