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How to use it?
- Derivative of:
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Derivative of 1/3*x^3
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Derivative of x*x^(1/2)
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Derivative of x^(5/2)
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Derivative of (x-4)^2
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Identical expressions
- arccos((sqrt(x))/(one +x))
- arc co sinus of e of (( square root of (x)) divide by (1 plus x))
- arc co sinus of e of (( square root of (x)) divide by (one plus x))
- arccos((√(x))/(1+x))
- arccossqrtx/1+x
- arccos((sqrt(x)) divide by (1+x))
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Similar expressions
- arccos((sqrt(x))/(1-x))
Derivative of arccos((sqrt(x))/(1+x))
The solution
You have entered
[src]
/ ___\
|\/ x |
acos|-----|
\1 + x/
$$\operatorname{acos}{\left(\frac{\sqrt{x}}{x + 1} \right)}$$
acos(sqrt(x)/(1 + x))
The first derivative
[src]
/ ___ \
| 1 \/ x |
-|--------------- - --------|
| ___ 2|
\2*\/ x *(1 + x) (1 + x) /
------------------------------
______________
/ x
/ 1 - --------
/ 2
\/ (1 + x)
$$- \frac{- \frac{\sqrt{x}}{\left(x + 1\right)^{2}} + \frac{1}{2 \sqrt{x} \left(x + 1\right)}}{\sqrt{- \frac{x}{\left(x + 1\right)^{2}} + 1}}$$
The second derivative
[src]
/ ___\
/ 2*x \ | 1 2*\/ x |
|-1 + -----|*|- ----- + -------|
___ \ 1 + x/ | ___ 1 + x |
1 1 2*\/ x \ \/ x /
------ + ------------- - -------- - --------------------------------
3/2 ___ 2 2 / x \
4*x \/ x *(1 + x) (1 + x) 4*(1 + x) *|1 - --------|
| 2|
\ (1 + x) /
--------------------------------------------------------------------
______________
/ x
(1 + x)* / 1 - --------
/ 2
\/ (1 + x)
$$\frac{- \frac{2 \sqrt{x}}{\left(x + 1\right)^{2}} - \frac{\left(\frac{2 \sqrt{x}}{x + 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x + 1} - 1\right)}{4 \left(x + 1\right)^{2} \left(- \frac{x}{\left(x + 1\right)^{2}} + 1\right)} + \frac{1}{\sqrt{x} \left(x + 1\right)} + \frac{1}{4 x^{\frac{3}{2}}}}{\left(x + 1\right) \sqrt{- \frac{x}{\left(x + 1\right)^{2}} + 1}}$$
The third derivative
[src]
/ ___\ / ___ \ 2 / ___\
/ 3*x \ | 1 2*\/ x | / 2*x \ | 1 8*\/ x 4 | / 2*x \ | 1 2*\/ x |
|-2 + -----|*|- ----- + -------| |-1 + -----|*|---- - -------- + -------------| 3*|-1 + -----| *|- ----- + -------|
___ \ 1 + x/ | ___ 1 + x | \ 1 + x/ | 3/2 2 ___ | \ 1 + x/ | ___ 1 + x |
3 3 6*\/ x 3 \ \/ x / \x (1 + x) \/ x *(1 + x)/ \ \/ x /
- ------ - -------------- + -------- - -------------- + -------------------------------- - ---------------------------------------------- + -----------------------------------
5/2 ___ 2 3 3/2 3 / x \ 2 / x \ 2
8*x \/ x *(1 + x) (1 + x) 4*x *(1 + x) 2*(1 + x) *|1 - --------| 4*(1 + x) *|1 - --------| 4 / x \
| 2| | 2| 8*(1 + x) *|1 - --------|
\ (1 + x) / \ (1 + x) / | 2|
\ (1 + x) /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
______________
/ x
(1 + x)* / 1 - --------
/ 2
\/ (1 + x)
$$\frac{\frac{6 \sqrt{x}}{\left(x + 1\right)^{3}} - \frac{\left(\frac{2 x}{x + 1} - 1\right) \left(- \frac{8 \sqrt{x}}{\left(x + 1\right)^{2}} + \frac{4}{\sqrt{x} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right)}{4 \left(x + 1\right)^{2} \left(- \frac{x}{\left(x + 1\right)^{2}} + 1\right)} + \frac{\left(\frac{2 \sqrt{x}}{x + 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{3 x}{x + 1} - 2\right)}{2 \left(x + 1\right)^{3} \left(- \frac{x}{\left(x + 1\right)^{2}} + 1\right)} + \frac{3 \left(\frac{2 \sqrt{x}}{x + 1} - \frac{1}{\sqrt{x}}\right) \left(\frac{2 x}{x + 1} - 1\right)^{2}}{8 \left(x + 1\right)^{4} \left(- \frac{x}{\left(x + 1\right)^{2}} + 1\right)^{2}} - \frac{3}{\sqrt{x} \left(x + 1\right)^{2}} - \frac{3}{4 x^{\frac{3}{2}} \left(x + 1\right)} - \frac{3}{8 x^{\frac{5}{2}}}}{\left(x + 1\right) \sqrt{- \frac{x}{\left(x + 1\right)^{2}} + 1}}$$