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 (x^5+1)
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Derivative of x^(4/3)
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Derivative of (x^2)/36
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Derivative of x+log(x)
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Identical expressions
- arcsin(√x)-√(x-x^ two)
- arc sinus of (√x) minus √(x minus x squared )
- arc sinus of (√x) minus √(x minus x to the power of two)
- arcsin(√x)-√(x-x2)
- arcsin√x-√x-x2
- arcsin(√x)-√(x-x²)
- arcsin(√x)-√(x-x to the power of 2)
- arcsin√x-√x-x^2
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Similar expressions
- arcsin(√x)-√(x+x^2)
- arcsin(√x)+√(x-x^2)
Derivative of arcsin(√x)-√(x-x^2)
The solution
You have entered
[src]
________
/ ___\ / 2
asin\\/ x / - \/ x - x
$$- \sqrt{- x^{2} + x} + \operatorname{asin}{\left(\sqrt{x} \right)}$$
asin(sqrt(x)) - sqrt(x - x^2)
The first derivative
[src]
1 1/2 - x
----------------- - -----------
___ _______ ________
2*\/ x *\/ 1 - x / 2
\/ x - x
$$- \frac{\frac{1}{2} - x}{\sqrt{- x^{2} + x}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x}}$$
The second derivative
[src]
2
1 1 1 (-1 + 2*x)
------------- - ---------------- + ------------------ + ----------------
___________ 3/2 _______ ___ 3/2 3/2
\/ x*(1 - x) 4*x *\/ 1 - x 4*\/ x *(1 - x) 4*(x*(1 - x))
$$\frac{1}{\sqrt{x \left(1 - x\right)}} + \frac{\left(2 x - 1\right)^{2}}{4 \left(x \left(1 - x\right)\right)^{\frac{3}{2}}} + \frac{1}{4 \sqrt{x} \left(1 - x\right)^{\frac{3}{2}}} - \frac{1}{4 x^{\frac{3}{2}} \sqrt{1 - x}}$$
The third derivative
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3
2 3 3 3*(-1 + 2*x) 12*(-1 + 2*x)
- --------------- + -------------- + ---------------- + -------------- + --------------
3/2 3/2 5/2 _______ ___ 5/2 5/2 3/2
x *(1 - x) x *\/ 1 - x \/ x *(1 - x) (x*(1 - x)) (x*(1 - x))
---------------------------------------------------------------------------------------
8
$$\frac{\frac{12 \left(2 x - 1\right)}{\left(x \left(1 - x\right)\right)^{\frac{3}{2}}} + \frac{3 \left(2 x - 1\right)^{3}}{\left(x \left(1 - x\right)\right)^{\frac{5}{2}}} + \frac{3}{\sqrt{x} \left(1 - x\right)^{\frac{5}{2}}} - \frac{2}{x^{\frac{3}{2}} \left(1 - x\right)^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}} \sqrt{1 - x}}}{8}$$