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How to use it?
- Derivative of:
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Derivative of 2/e^x
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Derivative of 3x²-2
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Derivative of 2*x/(x^2+4)
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Derivative of sqrt(x)-1/(sqrt(x)*2-x-1)
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Identical expressions
- (arctg(two x+ one))/(sin^2(x))
- (arctg(2x plus 1)) divide by ( sinus of squared (x))
- (arctg(two x plus one)) divide by ( sinus of squared (x))
- (arctg(2x+1))/(sin2(x))
- arctg2x+1/sin2x
- (arctg(2x+1))/(sin²(x))
- (arctg(2x+1))/(sin to the power of 2(x))
- arctg2x+1/sin^2x
- (arctg(2x+1)) divide by (sin^2(x))
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Similar expressions
- (arctg(2x-1))/(sin^2(x))
Derivative of (arctg(2x+1))/(sin^2(x))
The solution
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[src]
atan(2*x + 1)
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2
sin (x)
$$\frac{\operatorname{atan}{\left(2 x + 1 \right)}}{\sin^{2}{\left(x \right)}}$$
atan(2*x + 1)/sin(x)^2
The first derivative
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2 2*atan(2*x + 1)*cos(x) ------------------------ - ---------------------- / 2\ 2 3 \1 + (2*x + 1) /*sin (x) sin (x)
$$- \frac{2 \cos{\left(x \right)} \operatorname{atan}{\left(2 x + 1 \right)}}{\sin^{3}{\left(x \right)}} + \frac{2}{\left(\left(2 x + 1\right)^{2} + 1\right) \sin^{2}{\left(x \right)}}$$
The second derivative
[src]
// 2 \ \
|| 3*cos (x)| 4*(1 + 2*x) 4*cos(x) |
2*||1 + ---------|*atan(1 + 2*x) - ----------------- - -----------------------|
|| 2 | 2 / 2\ |
|\ sin (x) / / 2\ \1 + (1 + 2*x) /*sin(x)|
\ \1 + (1 + 2*x) / /
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2
sin (x)
$$\frac{2 \left(\left(1 + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \operatorname{atan}{\left(2 x + 1 \right)} - \frac{4 \left(2 x + 1\right)}{\left(\left(2 x + 1\right)^{2} + 1\right)^{2}} - \frac{4 \cos{\left(x \right)}}{\left(\left(2 x + 1\right)^{2} + 1\right) \sin{\left(x \right)}}\right)}{\sin^{2}{\left(x \right)}}$$
The third derivative
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/ / 2 \ / 2 \ / 2 \ \
| | 3*cos (x)| | 4*(1 + 2*x) | | 3*cos (x)| |
|3*|1 + ---------| 4*|-1 + --------------| 2*|2 + ---------|*atan(1 + 2*x)*cos(x) |
| | 2 | | 2| | 2 | |
| \ sin (x) / \ 1 + (1 + 2*x) / \ sin (x) / 12*(1 + 2*x)*cos(x) |
4*|----------------- + ----------------------- - -------------------------------------- + ------------------------|
| 2 2 sin(x) 2 |
| 1 + (1 + 2*x) / 2\ / 2\ |
\ \1 + (1 + 2*x) / \1 + (1 + 2*x) / *sin(x)/
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2
sin (x)
$$\frac{4 \left(\frac{3 \left(1 + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right)}{\left(2 x + 1\right)^{2} + 1} - \frac{2 \left(2 + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} \operatorname{atan}{\left(2 x + 1 \right)}}{\sin{\left(x \right)}} + \frac{12 \left(2 x + 1\right) \cos{\left(x \right)}}{\left(\left(2 x + 1\right)^{2} + 1\right)^{2} \sin{\left(x \right)}} + \frac{4 \left(\frac{4 \left(2 x + 1\right)^{2}}{\left(2 x + 1\right)^{2} + 1} - 1\right)}{\left(\left(2 x + 1\right)^{2} + 1\right)^{2}}\right)}{\sin^{2}{\left(x \right)}}$$