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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 x^-6
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Derivative of x^2*sqrt(1-x^2)
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Derivative of x^3*cot(x)
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Derivative of sin(x)+3
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Identical expressions
- fifteen *arcsin((x- one)/x)
- 15 multiply by arc sinus of ((x minus 1) divide by x)
- fifteen multiply by arc sinus of ((x minus one) divide by x)
- 15arcsin((x-1)/x)
- 15arcsinx-1/x
- 15*arcsin((x-1) divide by x)
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Similar expressions
- 15*arcsin((x+1)/x)
Derivative of 15*arcsin((x-1)/x)
The solution
You have entered
[src]
/x - 1\
15*asin|-----|
\ x /
$$15 \operatorname{asin}{\left(\frac{x - 1}{x} \right)}$$
15*asin((x - 1)/x)
The first derivative
[src]
/1 x - 1\
15*|- - -----|
|x 2 |
\ x /
--------------------
______________
/ 2
/ (x - 1)
/ 1 - --------
/ 2
\/ x
$$\frac{15 \left(\frac{1}{x} - \frac{x - 1}{x^{2}}\right)}{\sqrt{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}}}$$
The second derivative
[src]
/ / -1 + x\ \
| |1 - ------|*(-1 + x)|
/ -1 + x\ | \ x / |
-15*|1 - ------|*|2 - ---------------------|
\ x / | / 2\ |
| | (-1 + x) | |
| x*|1 - ---------| |
| | 2 | |
\ \ x / /
--------------------------------------------
_______________
/ 2
2 / (-1 + x)
x * / 1 - ---------
/ 2
\/ x
$$- \frac{15 \left(1 - \frac{x - 1}{x}\right) \left(2 - \frac{\left(1 - \frac{x - 1}{x}\right) \left(x - 1\right)}{x \left(1 - \frac{\left(x - 1\right)^{2}}{x^{2}}\right)}\right)}{x^{2} \sqrt{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}}}$$
The third derivative
[src]
/ 2 \
| 4*(-1 + x) 3*(-1 + x) 2 |
| 1 - ---------- + ----------- / -1 + x\ / -1 + x\ 2|
| x 2 4*|1 - ------|*(-1 + x) 3*|1 - ------| *(-1 + x) |
/ -1 + x\ | x \ x / \ x / |
15*|1 - ------|*|6 + ---------------------------- - ----------------------- + -------------------------|
\ x / | 2 / 2\ 2 |
| (-1 + x) | (-1 + x) | / 2\ |
| 1 - --------- x*|1 - ---------| 2 | (-1 + x) | |
| 2 | 2 | x *|1 - ---------| |
| x \ x / | 2 | |
\ \ x / /
--------------------------------------------------------------------------------------------------------
_______________
/ 2
3 / (-1 + x)
x * / 1 - ---------
/ 2
\/ x
$$\frac{15 \left(1 - \frac{x - 1}{x}\right) \left(6 + \frac{1 - \frac{4 \left(x - 1\right)}{x} + \frac{3 \left(x - 1\right)^{2}}{x^{2}}}{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}} - \frac{4 \left(1 - \frac{x - 1}{x}\right) \left(x - 1\right)}{x \left(1 - \frac{\left(x - 1\right)^{2}}{x^{2}}\right)} + \frac{3 \left(1 - \frac{x - 1}{x}\right)^{2} \left(x - 1\right)^{2}}{x^{2} \left(1 - \frac{\left(x - 1\right)^{2}}{x^{2}}\right)^{2}}\right)}{x^{3} \sqrt{1 - \frac{\left(x - 1\right)^{2}}{x^{2}}}}$$