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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 50/x
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Derivative of e^sin^2x
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Derivative of cos(x)-tan(x)
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Derivative of arsinx
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Identical expressions
- (arctgx)/(sqrt(2x- one))
- (arctgx) divide by ( square root of (2x minus 1))
- (arctgx) divide by ( square root of (2x minus one))
- (arctgx)/(√(2x-1))
- arctgx/sqrt2x-1
- (arctgx) divide by (sqrt(2x-1))
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Similar expressions
- (arctgx)/(sqrt(2x+1))
Derivative of (arctgx)/(sqrt(2x-1))
The solution
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[src]
acot(x) ----------- _________ \/ 2*x - 1
$$\frac{\operatorname{acot}{\left(x \right)}}{\sqrt{2 x - 1}}$$
acot(x)/sqrt(2*x - 1)
The first derivative
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1 acot(x) - -------------------- - ------------ / 2\ _________ 3/2 \1 + x /*\/ 2*x - 1 (2*x - 1)
$$- \frac{1}{\sqrt{2 x - 1} \left(x^{2} + 1\right)} - \frac{\operatorname{acot}{\left(x \right)}}{\left(2 x - 1\right)^{\frac{3}{2}}}$$
The second derivative
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2*x 2 3*acot(x)
--------- + ------------------- + -----------
2 / 2\ 2
/ 2\ \1 + x /*(-1 + 2*x) (-1 + 2*x)
\1 + x /
---------------------------------------------
__________
\/ -1 + 2*x
$$\frac{\frac{2 x}{\left(x^{2} + 1\right)^{2}} + \frac{2}{\left(2 x - 1\right) \left(x^{2} + 1\right)} + \frac{3 \operatorname{acot}{\left(x \right)}}{\left(2 x - 1\right)^{2}}}{\sqrt{2 x - 1}}$$
The third derivative
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/ / 2 \ \
| | 4*x | |
|2*|-1 + ------| |
| | 2| |
| \ 1 + x / 9 15*acot(x) 6*x |
-|--------------- + -------------------- + ----------- + --------------------|
| 2 / 2\ 2 3 2 |
| / 2\ \1 + x /*(-1 + 2*x) (-1 + 2*x) / 2\ |
\ \1 + x / \1 + x / *(-1 + 2*x)/
-------------------------------------------------------------------------------
__________
\/ -1 + 2*x
$$- \frac{\frac{6 x}{\left(2 x - 1\right) \left(x^{2} + 1\right)^{2}} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{9}{\left(2 x - 1\right)^{2} \left(x^{2} + 1\right)} + \frac{15 \operatorname{acot}{\left(x \right)}}{\left(2 x - 1\right)^{3}}}{\sqrt{2 x - 1}}$$