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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^(4/5)
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Derivative of x^3+2
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Derivative of x^2-7*x
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Derivative of ln(x)^2
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Identical expressions
- arctgx/sqrt(x)/(one +x^ two)
- arctgx divide by square root of (x) divide by (1 plus x squared )
- arctgx divide by square root of (x) divide by (one plus x to the power of two)
- arctgx/√(x)/(1+x^2)
- arctgx/sqrt(x)/(1+x2)
- arctgx/sqrtx/1+x2
- arctgx/sqrt(x)/(1+x²)
- arctgx/sqrt(x)/(1+x to the power of 2)
- arctgx/sqrtx/1+x^2
- arctgx divide by sqrt(x) divide by (1+x^2)
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Similar expressions
- arctgx/sqrt(x)/(1-x^2)
Derivative of arctgx/sqrt(x)/(1+x^2)
The solution
You have entered
[src]
acot(x) -------------- ___ / 2\ \/ x *\1 + x /
$$\frac{\operatorname{acot}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)}$$
d / acot(x) \ --|--------------| dx| ___ / 2\| \\/ x *\1 + x //
$$\frac{d}{d x} \frac{\operatorname{acot}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)}$$
The first derivative
[src]
1 acot(x) 2*x*acot(x)
- --------------- - --------------- - ---------------
2 3/2 / 2\ 2
___ / 2\ 2*x *\1 + x / ___ / 2\
\/ x *\1 + x / \/ x *\1 + x /
$$- \frac{2 x \operatorname{acot}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{1}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{\operatorname{acot}{\left(x \right)}}{2 x^{\frac{3}{2}} \left(x^{2} + 1\right)}$$
The second derivative
[src]
/ 2 \
| 4*x |
2*|-1 + ------|*acot(x)
___ | 2|
1 6*\/ x 3*acot(x) 2*acot(x) \ 1 + x /
------------- + --------- + --------- + -------------- + -----------------------
3/2 / 2\ 2 5/2 ___ / 2\ ___ / 2\
x *\1 + x / / 2\ 4*x \/ x *\1 + x / \/ x *\1 + x /
\1 + x /
--------------------------------------------------------------------------------
2
1 + x
$$\frac{\frac{2 \cdot \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{acot}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{6 \sqrt{x}}{\left(x^{2} + 1\right)^{2}} + \frac{2 \operatorname{acot}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{1}{x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3 \operatorname{acot}{\left(x \right)}}{4 x^{\frac{5}{2}}}}{x^{2} + 1}$$
The third derivative
[src]
/ / 2 \ / 2 \ / 2 \ \
| | 4*x | | 4*x | ___ | 2*x | |
| 8*|-1 + ------| 3*|-1 + ------|*acot(x) 24*\/ x *|-1 + ------|*acot(x)|
| 3/2 | 2| | 2| | 2| |
| 9 12*x 9 15*acot(x) \ 1 + x / 9*acot(x) \ 1 + x / \ 1 + x / |
-|--------------- + --------- + --------------- + ---------- + --------------- + --------------- + ----------------------- + ------------------------------|
| 2 3 5/2 / 2\ 7/2 2 3/2 / 2\ 3/2 / 2\ 2 |
| ___ / 2\ / 2\ 4*x *\1 + x / 8*x ___ / 2\ 2*x *\1 + x / x *\1 + x / / 2\ |
\\/ x *\1 + x / \1 + x / \/ x *\1 + x / \1 + x / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------
2
1 + x
$$- \frac{\frac{24 \sqrt{x} \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \operatorname{acot}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{12 x^{\frac{3}{2}}}{\left(x^{2} + 1\right)^{3}} + \frac{8 \cdot \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\sqrt{x} \left(x^{2} + 1\right)^{2}} + \frac{3 \cdot \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{acot}{\left(x \right)}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{9}{\sqrt{x} \left(x^{2} + 1\right)^{2}} + \frac{9 \operatorname{acot}{\left(x \right)}}{2 x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{9}{4 x^{\frac{5}{2}} \left(x^{2} + 1\right)} + \frac{15 \operatorname{acot}{\left(x \right)}}{8 x^{\frac{7}{2}}}}{x^{2} + 1}$$
The graph