Mister Exam
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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 6^(x^2-8x+28)
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Derivative of y=3x-4cbrt(x^3)+2^3
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Derivative of y=12cosx
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Derivative of x(x^2-5x+1)
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Identical expressions
- arcsin(x)/(one -x*x)^(one / two)
- arc sinus of (x) divide by (1 minus x multiply by x) to the power of (1 divide by 2)
- arc sinus of (x) divide by (one minus x multiply by x) to the power of (one divide by two)
- arcsin(x)/(1-x*x)(1/2)
- arcsinx/1-x*x1/2
- arcsin(x)/(1-xx)^(1/2)
- arcsin(x)/(1-xx)(1/2)
- arcsinx/1-xx1/2
- arcsinx/1-xx^1/2
- arcsin(x) divide by (1-x*x)^(1 divide by 2)
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Similar expressions
- arcsin(x)/(1+x*x)^(1/2)
- arcsinx/(1-x*x)^(1/2)
Derivative of arcsin(x)/(1-x*x)^(1/2)
The solution
You have entered
[src]
asin(x) ----------- _________ \/ 1 - x*x
$$\frac{\operatorname{asin}{\left(x \right)}}{\sqrt{- x x + 1}}$$
asin(x)/sqrt(1 - x*x)
The first derivative
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1 x*asin(x) ----------------------- + ------------ ________ 3/2 / 2 _________ (1 - x*x) \/ 1 - x *\/ 1 - x*x
$$\frac{x \operatorname{asin}{\left(x \right)}}{\left(- x x + 1\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{1 - x^{2}} \sqrt{- x x + 1}}$$
The second derivative
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/ 2 \
| 3*x |
|-1 + -------|*asin(x)
| 2|
3*x \ -1 + x /
--------- - ----------------------
2 3/2
/ 2\ / 2\
\1 - x / \1 - x /
$$\frac{3 x}{\left(1 - x^{2}\right)^{2}} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$$
The third derivative
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2 / 2 \ / 2 \
3*x | 3*x | | 5*x |
-1 + ------- 3*|-1 + -------| 3*x*|-3 + -------|*asin(x)
2 | 2| 2 | 2|
-1 + x \ -1 + x / 3*x \ -1 + x /
- ------------ - ---------------- + --------- - --------------------------
2 2 3 5/2
/ 2\ / 2\ / 2\ / 2\
\1 - x / \-1 + x / \1 - x / \1 - x /
$$\frac{3 x^{2}}{\left(1 - x^{2}\right)^{3}} - \frac{3 x \left(\frac{5 x^{2}}{x^{2} - 1} - 3\right) \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{3 \left(\frac{3 x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right)^{2}} - \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{2}}$$