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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
- Derivative of log(2)
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Derivative of log(x^-1)
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Derivative of cos(sqrt(x))
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Derivative of cos(1/x)
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Identical expressions
- 3x^ two *arcsin(2x- one)
- 3x squared multiply by arc sinus of (2x minus 1)
- 3x to the power of two multiply by arc sinus of (2x minus one)
- 3x2*arcsin(2x-1)
- 3x2*arcsin2x-1
- 3x²*arcsin(2x-1)
- 3x to the power of 2*arcsin(2x-1)
- 3x^2arcsin(2x-1)
- 3x2arcsin(2x-1)
- 3x2arcsin2x-1
- 3x^2arcsin2x-1
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Similar expressions
- 3x^2*arcsin(2x+1)
Derivative of 3x^2*arcsin(2x-1)
The solution
You have entered
[src]
2 3*x *asin(2*x - 1)
$$3 x^{2} \operatorname{asin}{\left(2 x - 1 \right)}$$
d / 2 \ --\3*x *asin(2*x - 1)/ dx
$$\frac{d}{d x} 3 x^{2} \operatorname{asin}{\left(2 x - 1 \right)}$$
The first derivative
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2
6*x
6*x*asin(2*x - 1) + -------------------
________________
/ 2
\/ 1 - (2*x - 1)
$$\frac{6 x^{2}}{\sqrt{1 - \left(2 x - 1\right)^{2}}} + 6 x \operatorname{asin}{\left(2 x - 1 \right)}$$
The second derivative
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/ 2 \ | 4*x 2*x *(-1 + 2*x) | 6*|-------------------- + -------------------- + asin(-1 + 2*x)| | _________________ 3/2 | | / 2 / 2\ | \\/ 1 - (-1 + 2*x) \1 - (-1 + 2*x) / /
$$6 \cdot \left(\frac{2 x^{2} \cdot \left(2 x - 1\right)}{\left(1 - \left(2 x - 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{4 x}{\sqrt{1 - \left(2 x - 1\right)^{2}}} + \operatorname{asin}{\left(2 x - 1 \right)}\right)$$
The third derivative
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/ / 2 \ \
| 2 | 3*(-1 + 2*x) | |
| 2*x *|-1 + ----------------| |
| | 2| |
| \ -1 + (-1 + 2*x) / 6*x*(-1 + 2*x)|
12*|3 - ---------------------------- + ---------------|
| 2 2|
\ 1 - (-1 + 2*x) 1 - (-1 + 2*x) /
-------------------------------------------------------
_________________
/ 2
\/ 1 - (-1 + 2*x)
$$\frac{12 \left(- \frac{2 x^{2} \cdot \left(\frac{3 \left(2 x - 1\right)^{2}}{\left(2 x - 1\right)^{2} - 1} - 1\right)}{1 - \left(2 x - 1\right)^{2}} + \frac{6 x \left(2 x - 1\right)}{1 - \left(2 x - 1\right)^{2}} + 3\right)}{\sqrt{1 - \left(2 x - 1\right)^{2}}}$$
The graph