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 (x^2-4)^3
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Derivative of 7*x+5
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Derivative of x/(x^4-3*x)
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Derivative of x^3*(x^2-1)^2
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Identical expressions
- arctg(sqrt(lnx))
- arctg( square root of (lnx))
- arctg(√(lnx))
- arctgsqrtlnx
Derivative of arctg(sqrt(lnx))
The solution
You have entered
[src]
/ ________\ atan\\/ log(x) /
$$\operatorname{atan}{\left(\sqrt{\log{\left(x \right)}} \right)}$$
atan(sqrt(log(x)))
The first derivative
[src]
1
---------------------------
________
2*x*(1 + log(x))*\/ log(x)
$$\frac{1}{2 x \left(\log{\left(x \right)} + 1\right) \sqrt{\log{\left(x \right)}}}$$
The second derivative
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/ 1 2 \ -|2 + ------ + ----------| \ log(x) 1 + log(x)/ ---------------------------- 2 ________ 4*x *(1 + log(x))*\/ log(x)
$$- \frac{2 + \frac{1}{\log{\left(x \right)}} + \frac{2}{\log{\left(x \right)} + 1}}{4 x^{2} \left(\log{\left(x \right)} + 1\right) \sqrt{\log{\left(x \right)}}}$$
The third derivative
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1 3 3 3 1
1 + ------------- + -------------- + -------- + --------- + ---------------------
2 2*(1 + log(x)) 4*log(x) 2 2*(1 + log(x))*log(x)
(1 + log(x)) 8*log (x)
---------------------------------------------------------------------------------
3 ________
x *(1 + log(x))*\/ log(x)
$$\frac{1 + \frac{3}{4 \log{\left(x \right)}} + \frac{3}{8 \log{\left(x \right)}^{2}} + \frac{3}{2 \left(\log{\left(x \right)} + 1\right)} + \frac{1}{2 \left(\log{\left(x \right)} + 1\right) \log{\left(x \right)}} + \frac{1}{\left(\log{\left(x \right)} + 1\right)^{2}}}{x^{3} \left(\log{\left(x \right)} + 1\right) \sqrt{\log{\left(x \right)}}}$$