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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of x^(7/6)
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Derivative of sec2x
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Derivative of f(x)=2x+3
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Derivative of e^x-7
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Identical expressions
- arcctgx*sin3x
- arcctgx multiply by sinus of 3x
- arcctgxsin3x
Derivative of arcctgx*sin3x
The solution
You have entered
[src]
acot(x)*sin(3*x)
$$\sin{\left(3 x \right)} \operatorname{acot}{\left(x \right)}$$
acot(x)*sin(3*x)
The first derivative
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sin(3*x)
- -------- + 3*acot(x)*cos(3*x)
2
1 + x
$$3 \cos{\left(3 x \right)} \operatorname{acot}{\left(x \right)} - \frac{\sin{\left(3 x \right)}}{x^{2} + 1}$$
The second derivative
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6*cos(3*x) 2*x*sin(3*x)
-9*acot(x)*sin(3*x) - ---------- + ------------
2 2
1 + x / 2\
\1 + x /
$$\frac{2 x \sin{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}} - 9 \sin{\left(3 x \right)} \operatorname{acot}{\left(x \right)} - \frac{6 \cos{\left(3 x \right)}}{x^{2} + 1}$$
The third derivative
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/ 2 \
| 4*x |
2*|-1 + ------|*sin(3*x)
| 2|
27*sin(3*x) \ 1 + x / 18*x*cos(3*x)
-27*acot(x)*cos(3*x) + ----------- - ------------------------ + -------------
2 2 2
1 + x / 2\ / 2\
\1 + x / \1 + x /
$$\frac{18 x \cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}} - 27 \cos{\left(3 x \right)} \operatorname{acot}{\left(x \right)} + \frac{27 \sin{\left(3 x \right)}}{x^{2} + 1} - \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \sin{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}}$$