Mister Exam
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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of (x-2)^4
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Derivative of (x-2)^2*(x-4)+5
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Derivative of e^x*x^3
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Derivative of 3*cos(x)
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Identical expressions
- y=sqrt(arctgx/ three)
- y equally square root of (arctgx divide by 3)
- y equally square root of (arctgx divide by three)
- y=√(arctgx/3)
- y=sqrtarctgx/3
- y=sqrt(arctgx divide by 3)
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Similar expressions
- y=sqrt(arctg(x/3))
Derivative of y=sqrt(arctgx/3)
The solution
You have entered
[src]
_________ / acot(x) / ------- \/ 3
$$\sqrt{\frac{\operatorname{acot}{\left(x \right)}}{3}}$$
sqrt(acot(x)/3)
The first derivative
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___ _________
\/ 3 *\/ acot(x)
- -----------------
3
--------------------
/ 2\
2*\1 + x /*acot(x)
$$- \frac{\frac{1}{3} \sqrt{3} \sqrt{\operatorname{acot}{\left(x \right)}}}{2 \left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}$$
The second derivative
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___ / 1 \
\/ 3 *|- ------- + 4*x|
\ acot(x) /
------------------------
2
/ 2\ _________
12*\1 + x / *\/ acot(x)
$$\frac{\sqrt{3} \left(4 x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right)}{12 \left(x^{2} + 1\right)^{2} \sqrt{\operatorname{acot}{\left(x \right)}}}$$
The third derivative
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/ 2 \
___ | 32*x 3 12*x |
\/ 3 *|8 - ------ - ----------------- + ----------------|
| 2 / 2\ 2 / 2\ |
\ 1 + x \1 + x /*acot (x) \1 + x /*acot(x)/
---------------------------------------------------------
2
/ 2\ _________
24*\1 + x / *\/ acot(x)
$$\frac{\sqrt{3} \left(- \frac{32 x^{2}}{x^{2} + 1} + \frac{12 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + 8 - \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right)}{24 \left(x^{2} + 1\right)^{2} \sqrt{\operatorname{acot}{\left(x \right)}}}$$
The graph