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 5x-1
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Derivative of 4*x^4
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Derivative of 3e^x
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Derivative of 2*y
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Identical expressions
- ln(arctan(sqrtx))
- ln(arc tangent of ( square root of x))
- ln(arctan(√x))
- lnarctansqrtx
Derivative of ln(arctan(sqrtx))
The solution
You have entered
[src]
/ / ___\\ log\atan\\/ x //
$$\log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)}$$
log(atan(sqrt(x)))
The first derivative
[src]
1
---------------------------
___ / ___\
2*\/ x *(1 + x)*atan\\/ x /
$$\frac{1}{2 \sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}$$
The second derivative
[src]
/ 1 2 1 \
-|---- + ------------- + ---------------------|
| 3/2 ___ / ___\|
\x \/ x *(1 + x) x*(1 + x)*atan\\/ x //
------------------------------------------------
/ ___\
4*(1 + x)*atan\\/ x /
$$- \frac{\frac{1}{x \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{2}{\sqrt{x} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}}}}{4 \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}$$
The third derivative
[src]
3 1 1 1 3 3
------ + -------------- + -------------- + ---------------------------- + ------------------------ + ------------------------
5/2 ___ 2 3/2 3/2 2 2/ ___\ 2 / ___\ 2 / ___\
8*x \/ x *(1 + x) 2*x *(1 + x) 4*x *(1 + x) *atan \\/ x / 4*x*(1 + x) *atan\\/ x / 8*x *(1 + x)*atan\\/ x /
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/ ___\
(1 + x)*atan\\/ x /
$$\frac{\frac{3}{4 x \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{3}{8 x^{2} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{1}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{1}{2 x^{\frac{3}{2}} \left(x + 1\right)} + \frac{1}{4 x^{\frac{3}{2}} \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} + \frac{3}{8 x^{\frac{5}{2}}}}{\left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}$$