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- Derivative of:
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Derivative of (x^2+1)^3
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Derivative of (x+3)/(x-2)
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Derivative of u
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Derivative of (x-1)/2
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Identical expressions
- sin⁴ three x*arctg2x^3
- sinus of ⁴3x multiply by arctg2x cubed
- sinus of ⁴ three x multiply by arctg2x cubed
- sin⁴3x*arctg2x3
- sin⁴3x*arctg2x³
- sin⁴3x*arctg2x to the power of 3
- sin⁴3xarctg2x^3
- sin⁴3xarctg2x3
Derivative of sin⁴3x*arctg2x^3
The solution
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[src]
43 3 sin (x)*atan (2*x)
$$\sin^{43}{\left(x \right)} \operatorname{atan}^{3}{\left(2 x \right)}$$
d / 43 3 \ --\sin (x)*atan (2*x)/ dx
$$\frac{d}{d x} \sin^{43}{\left(x \right)} \operatorname{atan}^{3}{\left(2 x \right)}$$
The first derivative
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2 43
6*atan (2*x)*sin (x) 3 42
--------------------- + 43*atan (2*x)*sin (x)*cos(x)
2
1 + 4*x
$$43 \sin^{42}{\left(x \right)} \cos{\left(x \right)} \operatorname{atan}^{3}{\left(2 x \right)} + \frac{6 \sin^{43}{\left(x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1}$$
The second derivative
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/ 2 \
41 | 2 / 2 2 \ 24*sin (x)*(-1 + 2*x*atan(2*x)) 516*atan(2*x)*cos(x)*sin(x)|
sin (x)*|- 43*atan (2*x)*\sin (x) - 42*cos (x)/ - ------------------------------- + ---------------------------|*atan(2*x)
| 2 2 |
| / 2\ 1 + 4*x |
\ \1 + 4*x / /
$$\left(- 43 \left(\sin^{2}{\left(x \right)} - 42 \cos^{2}{\left(x \right)}\right) \operatorname{atan}^{2}{\left(2 x \right)} + \frac{516 \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{24 \cdot \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin^{41}{\left(x \right)} \operatorname{atan}{\left(2 x \right)}$$
The third derivative
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/ / 2 2 \ \
| 3 | 1 2 12*x*atan(2*x) 16*x *atan (2*x)| |
| 48*sin (x)*|-------- - atan (2*x) - -------------- + ----------------| |
| | 2 2 2 | 2 / 2 2 \ 2 |
40 | 3 / 2 2 \ \1 + 4*x 1 + 4*x 1 + 4*x / 774*atan (2*x)*\sin (x) - 42*cos (x)/*sin(x) 3096*sin (x)*(-1 + 2*x*atan(2*x))*atan(2*x)*cos(x)|
sin (x)*|- 43*atan (2*x)*\- 1722*cos (x) + 127*sin (x)/*cos(x) + ---------------------------------------------------------------------- - -------------------------------------------- - --------------------------------------------------|
| 2 2 2 |
| / 2\ 1 + 4*x / 2\ |
\ \1 + 4*x / \1 + 4*x / /
$$\left(- 43 \cdot \left(127 \sin^{2}{\left(x \right)} - 1722 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)} \operatorname{atan}^{3}{\left(2 x \right)} - \frac{774 \left(\sin^{2}{\left(x \right)} - 42 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{3096 \cdot \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \sin^{2}{\left(x \right)} \cos{\left(x \right)} \operatorname{atan}{\left(2 x \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{48 \cdot \left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) \sin^{3}{\left(x \right)}}{\left(4 x^{2} + 1\right)^{2}}\right) \sin^{40}{\left(x \right)}$$
The graph