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 7x
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Derivative of 4/x^3
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Derivative of 4*sqrt(x)
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Derivative of -(3*pi*cos(pi*t/6))/2
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Identical expressions
- arcsin^ two (sqrt(x))
- arc sinus of squared ( square root of (x))
- arc sinus of to the power of two ( square root of (x))
- arcsin^2(√(x))
- arcsin2(sqrt(x))
- arcsin2sqrtx
- arcsin²(sqrt(x))
- arcsin to the power of 2(sqrt(x))
- arcsin^2sqrtx
Derivative of arcsin^2(sqrt(x))
The solution
You have entered
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2/ ___\ asin \\/ x /
$$\operatorname{asin}^{2}{\left(\sqrt{x} \right)}$$
d / 2/ ___\\ --\asin \\/ x // dx
$$\frac{d}{d x} \operatorname{asin}^{2}{\left(\sqrt{x} \right)}$$
The first derivative
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/ ___\ asin\\/ x / --------------- ___ _______ \/ x *\/ 1 - x
$$\frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\sqrt{x} \sqrt{- x + 1}}$$
The second derivative
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/ ___\ / ___\
1 asin\\/ x / asin\\/ x /
- ---------- + ---------------- - --------------
x*(-1 + x) ___ 3/2 3/2 _______
\/ x *(1 - x) x *\/ 1 - x
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2
$$\frac{- \frac{1}{x \left(x - 1\right)} + \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{\sqrt{x} \left(- x + 1\right)^{\frac{3}{2}}} - \frac{\operatorname{asin}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sqrt{- x + 1}}}{2}$$
The third derivative
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/ ___\ / ___\ / ___\
3 3 2*asin\\/ x / 3*asin\\/ x / 3*asin\\/ x /
----------- + ----------- - --------------- + -------------- + ----------------
2 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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4
$$\frac{\frac{3}{x \left(x - 1\right)^{2}} + \frac{3}{x^{2} \left(x - 1\right)} + \frac{3 \operatorname{asin}{\left(\sqrt{x} \right)}}{\sqrt{x} \left(- x + 1\right)^{\frac{5}{2}}} - \frac{2 \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \left(- x + 1\right)^{\frac{3}{2}}} + \frac{3 \operatorname{asin}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}} \sqrt{- x + 1}}}{4}$$
The graph