Mister Exam
Other calculators
- 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
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of ln(1+x)
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Derivative of sqrt(y)
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Derivative of e^sin(x)
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Derivative of e^(-2*x)
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Identical expressions
- arcsin(sqrt(x)+ one)
- arc sinus of ( square root of (x) plus 1)
- arc sinus of ( square root of (x) plus one)
- arcsin(√(x)+1)
- arcsinsqrtx+1
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Similar expressions
- arcsin(sqrt(x)-1)
Derivative of arcsin(sqrt(x)+1)
The solution
You have entered
[src]
/ ___ \ asin\\/ x + 1/
$$\operatorname{asin}{\left(\sqrt{x} + 1 \right)}$$
asin(sqrt(x) + 1)
The first derivative
[src]
1
------------------------------
__________________
/ 2
___ / / ___ \
2*\/ x *\/ 1 - \\/ x + 1/
$$\frac{1}{2 \sqrt{x} \sqrt{1 - \left(\sqrt{x} + 1\right)^{2}}}$$
The second derivative
[src]
___
1 1 + \/ x
- ---- + --------------------
3/2 / 2\
x | / ___\ |
x*\1 - \1 + \/ x / /
-----------------------------
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/ 2
/ / ___\
4*\/ 1 - \1 + \/ x /
$$\frac{\frac{\sqrt{x} + 1}{x \left(1 - \left(\sqrt{x} + 1\right)^{2}\right)} - \frac{1}{x^{\frac{3}{2}}}}{4 \sqrt{1 - \left(\sqrt{x} + 1\right)^{2}}}$$
The third derivative
[src]
2
/ ___\ / ___\
3 1 3*\1 + \/ x / 3*\1 + \/ x /
---- + ----------------------- - --------------------- + ------------------------
5/2 / 2\ / 2\ 2
x 3/2 | / ___\ | 2 | / ___\ | / 2\
x *\1 - \1 + \/ x / / x *\1 - \1 + \/ x / / 3/2 | / ___\ |
x *\1 - \1 + \/ x / /
---------------------------------------------------------------------------------
__________________
/ 2
/ / ___\
8*\/ 1 - \1 + \/ x /
$$\frac{- \frac{3 \left(\sqrt{x} + 1\right)}{x^{2} \left(1 - \left(\sqrt{x} + 1\right)^{2}\right)} + \frac{1}{x^{\frac{3}{2}} \left(1 - \left(\sqrt{x} + 1\right)^{2}\right)} + \frac{3 \left(\sqrt{x} + 1\right)^{2}}{x^{\frac{3}{2}} \left(1 - \left(\sqrt{x} + 1\right)^{2}\right)^{2}} + \frac{3}{x^{\frac{5}{2}}}}{8 \sqrt{1 - \left(\sqrt{x} + 1\right)^{2}}}$$