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- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of (x+5)/(x+1)
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Derivative of x*2^x
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Derivative of e^sin(x)*cos(x)
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Derivative of atan(3*x)
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Identical expressions
- asin(sqrt(x*a))
- arc sinus of e of ( square root of (x multiply by a))
- asin(√(x*a))
- asin(sqrt(xa))
- asinsqrtxa
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Similar expressions
- arcsin(sqrt(x*a))
Derivative of asin(sqrt(x*a))
The solution
You have entered
[src]
/ _____\ asin\\/ x*a /
$$\operatorname{asin}{\left(\sqrt{a x} \right)}$$
asin(sqrt(x*a))
The first derivative
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_____
\/ a*x
---------------
_________
2*x*\/ 1 - x*a
$$\frac{\sqrt{a x}}{2 x \sqrt{- a x + 1}}$$
The second derivative
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_____ / 1 a \
\/ a*x *|- - + -------|
\ x 1 - a*x/
-----------------------
_________
4*x*\/ 1 - a*x
$$\frac{\sqrt{a x} \left(\frac{a}{- a x + 1} - \frac{1}{x}\right)}{4 x \sqrt{- a x + 1}}$$
The third derivative
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/ 2 \
_____ |3 3*a 2*a |
\/ a*x *|-- + ---------- - -----------|
| 2 2 x*(1 - a*x)|
\x (1 - a*x) /
---------------------------------------
_________
8*x*\/ 1 - a*x
$$\frac{\sqrt{a x} \left(\frac{3 a^{2}}{\left(- a x + 1\right)^{2}} - \frac{2 a}{x \left(- a x + 1\right)} + \frac{3}{x^{2}}\right)}{8 x \sqrt{- a x + 1}}$$