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- Derivative of:
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Derivative of 5*x^4-7*x^2-x
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Derivative of e^(sin(1-3*x)^(2))
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Derivative of 3x-ln(x+3)^3
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Derivative of 3*e^(2*x)
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Identical expressions
- sin^ three (7x)*arcctg5x^ two
- sinus of cubed (7x) multiply by arcctg5x squared
- sinus of to the power of three (7x) multiply by arcctg5x to the power of two
- sin3(7x)*arcctg5x2
- sin37x*arcctg5x2
- sin³(7x)*arcctg5x²
- sin to the power of 3(7x)*arcctg5x to the power of 2
- sin^3(7x)arcctg5x^2
- sin3(7x)arcctg5x2
- sin37xarcctg5x2
- sin^37xarcctg5x^2
Derivative of sin^3(7x)*arcctg5x^2
The solution
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[src]
3 2 sin (7*x)*acot (5*x)
$$\sin^{3}{\left(7 x \right)} \operatorname{acot}^{2}{\left(5 x \right)}$$
sin(7*x)^3*acot(5*x)^2
The first derivative
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3
10*sin (7*x)*acot(5*x) 2 2
- ---------------------- + 21*acot (5*x)*sin (7*x)*cos(7*x)
2
1 + 25*x
$$21 \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)} \operatorname{acot}^{2}{\left(5 x \right)} - \frac{10 \sin^{3}{\left(7 x \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1}$$
The second derivative
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/ 2 \ | 2 / 2 2 \ 50*sin (7*x)*(1 + 10*x*acot(5*x)) 420*acot(5*x)*cos(7*x)*sin(7*x)| |- 147*acot (5*x)*\sin (7*x) - 2*cos (7*x)/ + --------------------------------- - -------------------------------|*sin(7*x) | 2 2 | | / 2\ 1 + 25*x | \ \1 + 25*x / /
$$\left(- 147 \left(\sin^{2}{\left(7 x \right)} - 2 \cos^{2}{\left(7 x \right)}\right) \operatorname{acot}^{2}{\left(5 x \right)} - \frac{420 \sin{\left(7 x \right)} \cos{\left(7 x \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{50 \left(10 x \operatorname{acot}{\left(5 x \right)} + 1\right) \sin^{2}{\left(7 x \right)}}{\left(25 x^{2} + 1\right)^{2}}\right) \sin{\left(7 x \right)}$$
The third derivative
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/ 2 \
3 | 15*x 100*x *acot(5*x)|
500*sin (7*x)*|-acot(5*x) + --------- + ----------------|
| 2 2 | 2 / 2 2 \
2 / 2 2 \ \ 1 + 25*x 1 + 25*x / 3150*sin (7*x)*(1 + 10*x*acot(5*x))*cos(7*x) 4410*\sin (7*x) - 2*cos (7*x)/*acot(5*x)*sin(7*x)
- 1029*acot (5*x)*\- 2*cos (7*x) + 7*sin (7*x)/*cos(7*x) - --------------------------------------------------------- + -------------------------------------------- + -------------------------------------------------
2 2 2
/ 2\ / 2\ 1 + 25*x
\1 + 25*x / \1 + 25*x /
$$- 1029 \left(7 \sin^{2}{\left(7 x \right)} - 2 \cos^{2}{\left(7 x \right)}\right) \cos{\left(7 x \right)} \operatorname{acot}^{2}{\left(5 x \right)} + \frac{4410 \left(\sin^{2}{\left(7 x \right)} - 2 \cos^{2}{\left(7 x \right)}\right) \sin{\left(7 x \right)} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{3150 \left(10 x \operatorname{acot}{\left(5 x \right)} + 1\right) \sin^{2}{\left(7 x \right)} \cos{\left(7 x \right)}}{\left(25 x^{2} + 1\right)^{2}} - \frac{500 \left(\frac{100 x^{2} \operatorname{acot}{\left(5 x \right)}}{25 x^{2} + 1} + \frac{15 x}{25 x^{2} + 1} - \operatorname{acot}{\left(5 x \right)}\right) \sin^{3}{\left(7 x \right)}}{\left(25 x^{2} + 1\right)^{2}}$$