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