Differentiate w.r.t. x
27x\left(-x^{2}\cos(3x)-x\sin(3x)+3x\cos(3x)+2\sin(3x)\right)
Evaluate
9\left(3-x\right)x^{2}\sin(3x)
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\frac{\mathrm{d}}{\mathrm{d}x}(\left(27x^{2}-9x^{3}\right)\sin(3x))
Use the distributive property to multiply 9x^{2} by 3-x.
\frac{\mathrm{d}}{\mathrm{d}x}(27x^{2}\sin(3x)-9x^{3}\sin(3x))
Use the distributive property to multiply 27x^{2}-9x^{3} by \sin(3x).
2\times 27\sin(3x)x^{2-1}+3\left(-9\sin(3x)\right)x^{3-1}
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}.
54\sin(3x)x^{2-1}+3\left(-9\sin(3x)\right)x^{3-1}
Multiply 2 times 27\sin(3x).
54\sin(3x)x^{1}+3\left(-9\sin(3x)\right)x^{3-1}
Subtract 1 from 2.
54\sin(3x)x^{1}+\left(-27\sin(3x)\right)x^{3-1}
Multiply 3 times -9\sin(3x).
54\sin(3x)x^{1}+\left(-27\sin(3x)\right)x^{2}
Subtract 1 from 3.
54\sin(3x)x+\left(-27\sin(3x)\right)x^{2}
For any term t, t^{1}=t.
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}