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
-
How to use it?
- Derivative of:
-
Derivative of x^-2
-
Derivative of x+3
-
Derivative of asin(x)
-
Derivative of (-1)/x^2
-
Identical expressions
- one / three *ln(ctg(x)+ one)- one / six *ln(ctg^ two (x)-ctg(x)+ one)- two * three ^(one / two)*arctg((two ctg(x)- one)/(three ^(one /2)))
- 1 divide by 3 multiply by ln(ctg(x) plus 1) minus 1 divide by 6 multiply by ln(ctg squared (x) minus ctg(x) plus 1) minus 2 multiply by 3 to the power of (1 divide by 2) multiply by arctg((2ctg(x) minus 1) divide by (3 to the power of (1 divide by 2)))
- one divide by three multiply by ln(ctg(x) plus one) minus one divide by six multiply by ln(ctg to the power of two (x) minus ctg(x) plus one) minus two multiply by three to the power of (one divide by two) multiply by arctg((two ctg(x) minus one) divide by (three to the power of (one divide by 2)))
- 1/3*ln(ctg(x)+1)-1/6*ln(ctg2(x)-ctg(x)+1)-2*3(1/2)*arctg((2ctg(x)-1)/(3(1/2)))
- 1/3*lnctgx+1-1/6*lnctg2x-ctgx+1-2*31/2*arctg2ctgx-1/31/2
- 1/3*ln(ctg(x)+1)-1/6*ln(ctg²(x)-ctg(x)+1)-2*3^(1/2)*arctg((2ctg(x)-1)/(3^(1/2)))
- 1/3*ln(ctg(x)+1)-1/6*ln(ctg to the power of 2(x)-ctg(x)+1)-2*3 to the power of (1/2)*arctg((2ctg(x)-1)/(3 to the power of (1/2)))
- 1/3ln(ctg(x)+1)-1/6ln(ctg^2(x)-ctg(x)+1)-23^(1/2)arctg((2ctg(x)-1)/(3^(1/2)))
- 1/3ln(ctg(x)+1)-1/6ln(ctg2(x)-ctg(x)+1)-23(1/2)arctg((2ctg(x)-1)/(3(1/2)))
- 1/3lnctgx+1-1/6lnctg2x-ctgx+1-231/2arctg2ctgx-1/31/2
- 1/3lnctgx+1-1/6lnctg^2x-ctgx+1-23^1/2arctg2ctgx-1/3^1/2
- 1 divide by 3*ln(ctg(x)+1)-1 divide by 6*ln(ctg^2(x)-ctg(x)+1)-2*3^(1 divide by 2)*arctg((2ctg(x)-1) divide by (3^(1 divide by 2)))
-
Similar expressions
- 1/3*ln(ctg(x)+1)-1/6*ln(ctg^2(x)+ctg(x)+1)-2*3^(1/2)*arctg((2ctg(x)-1)/(3^(1/2)))
- 1/3*ln(ctg(x)+1)-1/6*ln(ctg^2(x)-ctg(x)-1)-2*3^(1/2)*arctg((2ctg(x)-1)/(3^(1/2)))
- 1/3*ln(ctg(x)+1)-1/6*ln(ctg^2(x)-ctg(x)+1)-2*3^(1/2)*arctg((2ctg(x)+1)/(3^(1/2)))
- 1/3*ln(ctg(x)+1)+1/6*ln(ctg^2(x)-ctg(x)+1)-2*3^(1/2)*arctg((2ctg(x)-1)/(3^(1/2)))
- 1/3*ln(ctg(x)+1)-1/6*ln(ctg^2(x)-ctg(x)+1)+2*3^(1/2)*arctg((2ctg(x)-1)/(3^(1/2)))
- 1/3*ln(ctg(x)-1)-1/6*ln(ctg^2(x)-ctg(x)+1)-2*3^(1/2)*arctg((2ctg(x)-1)/(3^(1/2)))
The derivative of the function/
1/3*ln(ctg(x)+1)-1/6*ln(ctg^2(x)-ctg(x)+1)-2*3^(1/2)*arctg((2ctg(x)-1)/(3^(1/2)))
Derivative of 1/3*ln(ctg(x)+1)-1/6*ln(ctg^2(x)-ctg(x)+1)-2*3^(1/2)*arctg((2ctg(x)-1)/(3^(1/2)))
The solution
You have entered
[src]
/ 2 \
log(cot(x) + 1) log\cot (x) - cot(x) + 1/ ___ /2*cot(x) - 1\
--------------- - ------------------------- - 2*\/ 3 *atan|------------|
3 6 | ___ |
\ \/ 3 /
$$\left(- \frac{\log{\left(\left(\cot^{2}{\left(x \right)} - \cot{\left(x \right)}\right) + 1 \right)}}{6} + \frac{\log{\left(\cot{\left(x \right)} + 1 \right)}}{3}\right) - 2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \cot{\left(x \right)} - 1}{\sqrt{3}} \right)}$$
log(cot(x) + 1)/3 - log(cot(x)^2 - cot(x) + 1)/6 - 2*sqrt(3)*atan((2*cot(x) - 1)/sqrt(3))
The first derivative
[src]
/ 2 \ 2 / 2 \ 2
2*\-2 - 2*cot (x)/ 1 + cot (x) + \-2 - 2*cot (x)/*cot(x) -1 - cot (x)
- ------------------- - ------------------------------------- + --------------
2 / 2 \ 3*(cot(x) + 1)
(2*cot(x) - 1) 6*\cot (x) - cot(x) + 1/
1 + ---------------
3
$$\frac{- \cot^{2}{\left(x \right)} - 1}{3 \left(\cot{\left(x \right)} + 1\right)} - \frac{\left(- 2 \cot^{2}{\left(x \right)} - 2\right) \cot{\left(x \right)} + \cot^{2}{\left(x \right)} + 1}{6 \left(\left(\cot^{2}{\left(x \right)} - \cot{\left(x \right)}\right) + 1\right)} - \frac{2 \left(- 2 \cot^{2}{\left(x \right)} - 2\right)}{\frac{\left(2 \cot{\left(x \right)} - 1\right)^{2}}{3} + 1}$$
The second derivative
[src]
2 2 2
/ 2 \ / 2 / 2 \ \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \
\1 + cot (x)/ \1 + cot (x) - 2*\1 + cot (x)/*cot(x)/ 24*\1 + cot (x)/*cot(x) 48*\1 + cot (x)/ *(-1 + 2*cot(x)) \1 + cot (x)/*\1 - cot(x) + 3*cot (x)/ 2*\1 + cot (x)/*cot(x)
- --------------- + --------------------------------------- - ----------------------- + --------------------------------- - -------------------------------------- + ----------------------
2 2 2 2 / 2 \ 3*(1 + cot(x))
3*(1 + cot(x)) / 2 \ 3 + (-1 + 2*cot(x)) / 2\ 3*\1 + cot (x) - cot(x)/
6*\1 + cot (x) - cot(x)/ \3 + (-1 + 2*cot(x)) /
$$- \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} - \cot{\left(x \right)} + 1\right)}{3 \left(\cot^{2}{\left(x \right)} - \cot{\left(x \right)} + 1\right)} + \frac{\left(- 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + \cot^{2}{\left(x \right)} + 1\right)^{2}}{6 \left(\cot^{2}{\left(x \right)} - \cot{\left(x \right)} + 1\right)^{2}} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{3 \left(\cot{\left(x \right)} + 1\right)} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{3 \left(\cot{\left(x \right)} + 1\right)^{2}} - \frac{24 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\left(2 \cot{\left(x \right)} - 1\right)^{2} + 3} + \frac{48 \left(2 \cot{\left(x \right)} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\left(\left(2 \cot{\left(x \right)} - 1\right)^{2} + 3\right)^{2}}$$
The third derivative
[src]
3 2 2 3 3 2 3 2
/ 2 \ / 2 \ / 2 \ / 2 \ / 2 / 2 \ \ / 2 \ 2 / 2 \ / 2 \ 2 2 / 2 \ / 2 \ / 2 3 / 2 \ \ / 2 \ / 2 / 2 \ \ / 2 \ / 2 \
96*\1 + cot (x)/ 24*\1 + cot (x)/ 2*\1 + cot (x)/ 2*\1 + cot (x)/ \1 + cot (x) - 2*\1 + cot (x)/*cot(x)/ 2*\1 + cot (x)/ *cot(x) 48*cot (x)*\1 + cot (x)/ 384*\1 + cot (x)/ *(-1 + 2*cot(x)) 4*cot (x)*\1 + cot (x)/ \1 + cot (x)/*\-1 - 3*cot (x) + 4*cot (x) + 8*\1 + cot (x)/*cot(x)/ \1 + cot (x)/*\1 + cot (x) - 2*\1 + cot (x)/*cot(x)/*\1 - cot(x) + 3*cot (x)/ 288*\1 + cot (x)/ *(-1 + 2*cot(x))*cot(x)
- ----------------------- + -------------------- - ---------------- - ---------------- - --------------------------------------- + ----------------------- + ------------------------ + ----------------------------------- - ----------------------- + ------------------------------------------------------------------- + ----------------------------------------------------------------------------- - -----------------------------------------
2 2 3*(1 + cot(x)) 3 3 2 2 3 3*(1 + cot(x)) / 2 \ 2 2
/ 2\ 3 + (-1 + 2*cot(x)) 3*(1 + cot(x)) / 2 \ (1 + cot(x)) 3 + (-1 + 2*cot(x)) / 2\ 3*\1 + cot (x) - cot(x)/ / 2 \ / 2\
\3 + (-1 + 2*cot(x)) / 3*\1 + cot (x) - cot(x)/ \3 + (-1 + 2*cot(x)) / \1 + cot (x) - cot(x)/ \3 + (-1 + 2*cot(x)) /
$$\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \left(- 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + \cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} - \cot{\left(x \right)} + 1\right)}{\left(\cot^{2}{\left(x \right)} - \cot{\left(x \right)} + 1\right)^{2}} + \frac{\left(\cot^{2}{\left(x \right)} + 1\right) \left(8 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + 4 \cot^{3}{\left(x \right)} - 3 \cot^{2}{\left(x \right)} - 1\right)}{3 \left(\cot^{2}{\left(x \right)} - \cot{\left(x \right)} + 1\right)} - \frac{\left(- 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + \cot^{2}{\left(x \right)} + 1\right)^{3}}{3 \left(\cot^{2}{\left(x \right)} - \cot{\left(x \right)} + 1\right)^{3}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{3 \left(\cot{\left(x \right)} + 1\right)} - \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)}}{3 \left(\cot{\left(x \right)} + 1\right)} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot{\left(x \right)}}{\left(\cot{\left(x \right)} + 1\right)^{2}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{3}}{3 \left(\cot{\left(x \right)} + 1\right)^{3}} + \frac{24 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\left(2 \cot{\left(x \right)} - 1\right)^{2} + 3} + \frac{48 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)}}{\left(2 \cot{\left(x \right)} - 1\right)^{2} + 3} - \frac{288 \left(2 \cot{\left(x \right)} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot{\left(x \right)}}{\left(\left(2 \cot{\left(x \right)} - 1\right)^{2} + 3\right)^{2}} - \frac{96 \left(\cot^{2}{\left(x \right)} + 1\right)^{3}}{\left(\left(2 \cot{\left(x \right)} - 1\right)^{2} + 3\right)^{2}} + \frac{384 \left(2 \cot{\left(x \right)} - 1\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right)^{3}}{\left(\left(2 \cot{\left(x \right)} - 1\right)^{2} + 3\right)^{3}}$$