Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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- Differential equations Step by Step
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How to use it?
- Derivative of:
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Derivative of (4-3*x)^7
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Derivative of 3x²-2
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Derivative of (x-5)^2*e^x-7
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Derivative of x/(1+e^x)
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Identical expressions
- sqrt(arctg(ln(x)+ one))
- square root of (arctg(ln(x) plus 1))
- square root of (arctg(ln(x) plus one))
- √(arctg(ln(x)+1))
- sqrtarctglnx+1
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Similar expressions
- sqrt(arctg(ln(x)-1))
Derivative of sqrt(arctg(ln(x)+1))
The solution
You have entered
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__________________ \/ atan(log(x) + 1)
$$\sqrt{\operatorname{atan}{\left(\log{\left(x \right)} + 1 \right)}}$$
sqrt(atan(log(x) + 1))
The first derivative
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1
--------------------------------------------
/ 2\ __________________
2*x*\1 + (log(x) + 1) /*\/ atan(log(x) + 1)
$$\frac{1}{2 x \left(\left(\log{\left(x \right)} + 1\right)^{2} + 1\right) \sqrt{\operatorname{atan}{\left(\log{\left(x \right)} + 1 \right)}}}$$
The second derivative
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/1 1 + log(x) 1 \
-|- + ----------------- + --------------------------------------|
|2 2 / 2\ |
\ 1 + (1 + log(x)) 4*\1 + (1 + log(x)) /*atan(1 + log(x))/
------------------------------------------------------------------
2 / 2\ __________________
x *\1 + (1 + log(x)) /*\/ atan(1 + log(x))
$$- \frac{\frac{1}{2} + \frac{\log{\left(x \right)} + 1}{\left(\log{\left(x \right)} + 1\right)^{2} + 1} + \frac{1}{4 \left(\left(\log{\left(x \right)} + 1\right)^{2} + 1\right) \operatorname{atan}{\left(\log{\left(x \right)} + 1 \right)}}}{x^{2} \left(\left(\log{\left(x \right)} + 1\right)^{2} + 1\right) \sqrt{\operatorname{atan}{\left(\log{\left(x \right)} + 1 \right)}}}$$
The third derivative
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2
1 3*(1 + log(x)) 4*(1 + log(x)) 3 3 3*(1 + log(x))
1 - ----------------- + ----------------- + -------------------- + -------------------------------------- + ---------------------------------------- + ---------------------------------------
2 2 2 / 2\ 2 2
1 + (1 + log(x)) 1 + (1 + log(x)) / 2\ 4*\1 + (1 + log(x)) /*atan(1 + log(x)) / 2\ 2 / 2\
\1 + (1 + log(x)) / 8*\1 + (1 + log(x)) / *atan (1 + log(x)) 2*\1 + (1 + log(x)) / *atan(1 + log(x))
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 / 2\ __________________
x *\1 + (1 + log(x)) /*\/ atan(1 + log(x))
$$\frac{1 + \frac{3 \left(\log{\left(x \right)} + 1\right)}{\left(\log{\left(x \right)} + 1\right)^{2} + 1} - \frac{1}{\left(\log{\left(x \right)} + 1\right)^{2} + 1} + \frac{3}{4 \left(\left(\log{\left(x \right)} + 1\right)^{2} + 1\right) \operatorname{atan}{\left(\log{\left(x \right)} + 1 \right)}} + \frac{4 \left(\log{\left(x \right)} + 1\right)^{2}}{\left(\left(\log{\left(x \right)} + 1\right)^{2} + 1\right)^{2}} + \frac{3 \left(\log{\left(x \right)} + 1\right)}{2 \left(\left(\log{\left(x \right)} + 1\right)^{2} + 1\right)^{2} \operatorname{atan}{\left(\log{\left(x \right)} + 1 \right)}} + \frac{3}{8 \left(\left(\log{\left(x \right)} + 1\right)^{2} + 1\right)^{2} \operatorname{atan}^{2}{\left(\log{\left(x \right)} + 1 \right)}}}{x^{3} \left(\left(\log{\left(x \right)} + 1\right)^{2} + 1\right) \sqrt{\operatorname{atan}{\left(\log{\left(x \right)} + 1 \right)}}}$$