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 6^x
-
Derivative of (x^2-1)/(x^2+1)
-
Derivative of (x+3)/(x-1)
-
Derivative of (x-3)^3
-
Identical expressions
- ln(coth(x/ two))
- ln( hyperbolic co tangent of gent of (x divide by 2))
- ln( hyperbolic co tangent of gent of (x divide by two))
- lncothx/2
- ln(coth(x divide by 2))
Derivative of ln(coth(x/2))
The solution
You have entered
[src]
/ /x\\ log|coth|-|| \ \2//
$$\log{\left(\coth{\left(\frac{x}{2} \right)} \right)}$$
d / / /x\\\ --|log|coth|-||| dx\ \ \2///
$$\frac{d}{d x} \log{\left(\coth{\left(\frac{x}{2} \right)} \right)}$$
The first derivative
[src]
-1
------------------
/x\ 2/x\
2*coth|-|*sinh |-|
\2/ \2/
$$- \frac{1}{2 \sinh^{2}{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}}$$
The second derivative
[src]
/x\ 1
2*cosh|-| - ---------------
\2/ /x\ /x\
coth|-|*sinh|-|
\2/ \2/
---------------------------
/x\ 3/x\
4*coth|-|*sinh |-|
\2/ \2/
$$\frac{2 \cosh{\left(\frac{x}{2} \right)} - \frac{1}{\sinh{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}}}{4 \sinh^{3}{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}}$$
The third derivative
[src]
2/x\ /x\
3*cosh |-| 3*cosh|-|
1 \2/ \2/
1 - ----------------- - ---------- + ----------------
2/x\ 4/x\ 2/x\ /x\ 3/x\
coth |-|*sinh |-| sinh |-| coth|-|*sinh |-|
\2/ \2/ \2/ \2/ \2/
-----------------------------------------------------
/x\ 2/x\
4*coth|-|*sinh |-|
\2/ \2/
$$\frac{1 - \frac{3 \cosh^{2}{\left(\frac{x}{2} \right)}}{\sinh^{2}{\left(\frac{x}{2} \right)}} + \frac{3 \cosh{\left(\frac{x}{2} \right)}}{\sinh^{3}{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}} - \frac{1}{\sinh^{4}{\left(\frac{x}{2} \right)} \coth^{2}{\left(\frac{x}{2} \right)}}}{4 \sinh^{2}{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}}$$
The graph