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How to use it?
- Derivative of:
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Derivative of y=4+6x-3x^4
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Derivative of √x+√x+√x
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Derivative of x*e^(-2x)
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Derivative of x+ln(x^2-4)
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Identical expressions
- arcsin(√x)+√(x-x^ two)
- arc sinus of (√x) plus √(x minus x squared )
- arc sinus of (√x) plus √(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
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1/2 - x 1 ----------- + ----------------- ________ ___ _______ / 2 2*\/ x *\/ 1 - x \/ x - x
$$\frac{\frac{1}{2} - x}{\sqrt{- x^{2} + x}} + \frac{1}{2 \sqrt{x} \sqrt{1 - x}}$$
The second derivative
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2
1 1 (-1 + 2*x) 1
- ------------- - ---------------- - ---------------- + ------------------
___________ 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
12*(-1 + 2*x) 3*(-1 + 2*x) 2 3 3
- -------------- - -------------- - --------------- + -------------- + ----------------
3/2 5/2 3/2 3/2 5/2 _______ ___ 5/2
(x*(1 - x)) (x*(1 - x)) x *(1 - x) x *\/ 1 - x \/ x *(1 - x)
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8
$$\frac{- \frac{12 \left(2 x - 1\right)}{\left(x \left(1 - x\right)\right)^{\frac{3}{2}}} - \frac{3 \left(2 x - 1\right)^{3}}{\left(x \left(1 - x\right)\right)^{\frac{5}{2}}} + \frac{3}{\sqrt{x} \left(1 - x\right)^{\frac{5}{2}}} - \frac{2}{x^{\frac{3}{2}} \left(1 - x\right)^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}} \sqrt{1 - x}}}{8}$$