Mister Exam
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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 tanh(x)
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Derivative of tanx
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Derivative of tg2x
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Derivative of 1-e^(-x)
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Identical expressions
- atan(sqrt(one +sqrt(x)))
- arc tangent of gent of ( square root of (1 plus square root of (x)))
- arc tangent of gent of ( square root of (one plus square root of (x)))
- atan(√(1+√(x)))
- atansqrt1+sqrtx
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Similar expressions
- atan(sqrt(1-sqrt(x)))
- arctan(sqrt(1+sqrt(x)))
Derivative of atan(sqrt(1+sqrt(x)))
The solution
You have entered
[src]
/ ___________\
| / ___ |
atan\\/ 1 + \/ x /
$$\operatorname{atan}{\left(\sqrt{\sqrt{x} + 1} \right)}$$
atan(sqrt(1 + sqrt(x)))
The first derivative
[src]
1
----------------------------------
___________
___ / ___ / ___\
4*\/ x *\/ 1 + \/ x *\2 + \/ x /
$$\frac{1}{4 \sqrt{x} \sqrt{\sqrt{x} + 1} \left(\sqrt{x} + 2\right)}$$
The second derivative
[src]
/ 2 1 2 \
-|---- + ------------- + -------------|
| 3/2 / ___\ / ___\|
\x x*\1 + \/ x / x*\2 + \/ x //
----------------------------------------
___________
/ ___ / ___\
16*\/ 1 + \/ x *\2 + \/ x /
$$- \frac{\frac{2}{x \left(\sqrt{x} + 2\right)} + \frac{1}{x \left(\sqrt{x} + 1\right)} + \frac{2}{x^{\frac{3}{2}}}}{16 \sqrt{\sqrt{x} + 1} \left(\sqrt{x} + 2\right)}$$
The third derivative
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12 3 6 8 12 4
---- + ----------------- + -------------- + ----------------- + -------------- + ----------------------------
5/2 2 2 / ___\ 2 2 / ___\ 3/2 / ___\ / ___\
x 3/2 / ___\ x *\1 + \/ x / 3/2 / ___\ x *\2 + \/ x / x *\1 + \/ x /*\2 + \/ x /
x *\1 + \/ x / x *\2 + \/ x /
-------------------------------------------------------------------------------------------------------------
___________
/ ___ / ___\
64*\/ 1 + \/ x *\2 + \/ x /
$$\frac{\frac{12}{x^{2} \left(\sqrt{x} + 2\right)} + \frac{6}{x^{2} \left(\sqrt{x} + 1\right)} + \frac{8}{x^{\frac{3}{2}} \left(\sqrt{x} + 2\right)^{2}} + \frac{4}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right) \left(\sqrt{x} + 2\right)} + \frac{3}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{12}{x^{\frac{5}{2}}}}{64 \sqrt{\sqrt{x} + 1} \left(\sqrt{x} + 2\right)}$$