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How to use it?
- Derivative of:
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Derivative of -x
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Derivative of sqrt(x)*sin(x)
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Derivative of arctg((tgx-ctgx)/sqrt(2))
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Derivative of y=sqrt((1+cosx)/(1-cosx))
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Identical expressions
- arctg((tgx-ctgx)/sqrt(two))
- arctg((tgx minus ctgx) divide by square root of (2))
- arctg((tgx minus ctgx) divide by square root of (two))
- arctg((tgx-ctgx)/√(2))
- arctgtgx-ctgx/sqrt2
- arctg((tgx-ctgx) divide by sqrt(2))
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Similar expressions
- arctg((tgx-ctgx)/sqrt(2)(2))
- arctg((tgx+ctgx)/sqrt(2))
Derivative of arctg((tgx-ctgx)/sqrt(2))
The solution
You have entered
[src]
/tan(x) - cot(x)\
atan|---------------|
| ___ |
\ \/ 2 /
$$\operatorname{atan}{\left(\frac{\tan{\left(x \right)} - \cot{\left(x \right)}}{\sqrt{2}} \right)}$$
d / /tan(x) - cot(x)\\ --|atan|---------------|| dx| | ___ || \ \ \/ 2 //
$$\frac{d}{d x} \operatorname{atan}{\left(\frac{\tan{\left(x \right)} - \cot{\left(x \right)}}{\sqrt{2}} \right)}$$
The first derivative
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___ / 2 2 \
\/ 2 *\2 + cot (x) + tan (x)/
-----------------------------
/ 2\
| (tan(x) - cot(x)) |
2*|1 + ------------------|
\ 2 /
$$\frac{\sqrt{2} \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)}{2 \left(\frac{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2}}{2} + 1\right)}$$
The second derivative
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/ 2 \
| / 2 2 \ |
___ |/ 2 \ / 2 \ \2 + cot (x) + tan (x)/ *(-cot(x) + tan(x))|
2*\/ 2 *|\1 + tan (x)/*tan(x) - \1 + cot (x)/*cot(x) - -------------------------------------------|
| 2 |
\ 2 + (-cot(x) + tan(x)) /
---------------------------------------------------------------------------------------------------
2
2 + (-cot(x) + tan(x))
$$\frac{2 \sqrt{2} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - \frac{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)^{2}}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2}\right)}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2}$$
The third derivative
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/ 3 3 \
| 2 2 / 2 2 \ 2 / 2 2 \ // 2 \ / 2 \ \ / 2 2 \|
___ |/ 2 \ / 2 \ \2 + cot (x) + tan (x)/ 2 / 2 \ 2 / 2 \ 4*(-cot(x) + tan(x)) *\2 + cot (x) + tan (x)/ 6*(-cot(x) + tan(x))*\\1 + tan (x)/*tan(x) - \1 + cot (x)/*cot(x)/*\2 + cot (x) + tan (x)/|
2*\/ 2 *|\1 + cot (x)/ + \1 + tan (x)/ - ------------------------ + 2*cot (x)*\1 + cot (x)/ + 2*tan (x)*\1 + tan (x)/ + ---------------------------------------------- - ------------------------------------------------------------------------------------------|
| 2 2 2 |
| 2 + (-cot(x) + tan(x)) / 2\ 2 + (-cot(x) + tan(x)) |
\ \2 + (-cot(x) + tan(x)) / /
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2
2 + (-cot(x) + tan(x))
$$\frac{2 \sqrt{2} \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} + \frac{4 \left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)^{3}}{\left(\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2\right)^{2}} - \frac{6 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right) \left(\tan{\left(x \right)} - \cot{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + \left(\cot^{2}{\left(x \right)} + 1\right)^{2} - \frac{\left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)} + 2\right)^{3}}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2}\right)}{\left(\tan{\left(x \right)} - \cot{\left(x \right)}\right)^{2} + 2}$$
The graph