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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of f(x)=2x-3
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Derivative of 2*cos(x)+sin(x)
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Derivative of (1-x^2)^10
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Derivative of (-1)/x+4*x^2
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Identical expressions
- arcsin((x+ one)/x^(one / two))
- arc sinus of ((x plus 1) divide by x to the power of (1 divide by 2))
- arc sinus of ((x plus one) divide by x to the power of (one divide by two))
- arcsin((x+1)/x(1/2))
- arcsinx+1/x1/2
- arcsinx+1/x^1/2
- arcsin((x+1) divide by x^(1 divide by 2))
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Similar expressions
- arcsin((x-1)/x^(1/2))
Derivative of arcsin((x+1)/x^(1/2))
The solution
You have entered
[src]
/x + 1\
asin|-----|
| ___|
\\/ x /
$$\operatorname{asin}{\left(\frac{x + 1}{\sqrt{x}} \right)}$$
asin((x + 1)/sqrt(x))
The first derivative
[src]
1 x + 1
----- - ------
___ 3/2
\/ x 2*x
-------------------
______________
/ 2
/ (x + 1)
/ 1 - --------
\/ x
$$\frac{\frac{1}{\sqrt{x}} - \frac{x + 1}{2 x^{\frac{3}{2}}}}{\sqrt{1 - \frac{\left(x + 1\right)^{2}}{x}}}$$
The second derivative
[src]
2
/ 1 + x\
|2 - -----| *(1 + x)
3*(1 + x) \ x /
-1 + --------- + --------------------
4*x / 2\
| (1 + x) |
4*|1 - --------|
\ x /
-------------------------------------
______________
/ 2
3/2 / (1 + x)
x * / 1 - --------
\/ x
$$\frac{-1 + \frac{\left(2 - \frac{x + 1}{x}\right)^{2} \left(x + 1\right)}{4 \left(1 - \frac{\left(x + 1\right)^{2}}{x}\right)} + \frac{3 \left(x + 1\right)}{4 x}}{x^{\frac{3}{2}} \sqrt{1 - \frac{\left(x + 1\right)^{2}}{x}}}$$
The third derivative
[src]
/ 2 \
/ 1 + x\ | (1 + x) 2*(1 + x)| 3
/ 5*(1 + x)\ 4*|2 - -----|*|1 + -------- - ---------| 2 / 1 + x\ / 1 + x\ / 3*(1 + x)\
3*|6 - ---------| \ x / | 2 x | 3*(1 + x) *|2 - -----| 2*(1 + x)*|2 - -----|*|4 - ---------|
\ x / \ x / \ x / \ x / \ x /
----------------- + ---------------------------------------- + ----------------------- - -------------------------------------
x 2 2 / 2\
(1 + x) / 2\ | (1 + x) |
1 - -------- | (1 + x) | x*|1 - --------|
x x*|1 - --------| \ x /
\ x /
------------------------------------------------------------------------------------------------------------------------------
______________
/ 2
3/2 / (1 + x)
8*x * / 1 - --------
\/ x
$$\frac{\frac{4 \left(2 - \frac{x + 1}{x}\right) \left(1 - \frac{2 \left(x + 1\right)}{x} + \frac{\left(x + 1\right)^{2}}{x^{2}}\right)}{1 - \frac{\left(x + 1\right)^{2}}{x}} + \frac{3 \left(6 - \frac{5 \left(x + 1\right)}{x}\right)}{x} - \frac{2 \left(2 - \frac{x + 1}{x}\right) \left(4 - \frac{3 \left(x + 1\right)}{x}\right) \left(x + 1\right)}{x \left(1 - \frac{\left(x + 1\right)^{2}}{x}\right)} + \frac{3 \left(2 - \frac{x + 1}{x}\right)^{3} \left(x + 1\right)^{2}}{x \left(1 - \frac{\left(x + 1\right)^{2}}{x}\right)^{2}}}{8 x^{\frac{3}{2}} \sqrt{1 - \frac{\left(x + 1\right)^{2}}{x}}}$$