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*e
-
Derivative of 7
-
Derivative of x^2sinx
-
Derivative of x-sqrt(x)
-
Identical expressions
- arcsec^- one (one /x)
- arcsec to the power of minus 1(1 divide by x)
- arcsec to the power of minus one (one divide by x)
- arcsec-1(1/x)
- arcsec-11/x
- arcsec^-11/x
- arcsec^-1(1 divide by x)
-
Similar expressions
- arcsec^+1(1/x)
Derivative of arcsec^-1(1/x)
The solution
You have entered
[src]
1
---------
/ 1\
asec|1*-|
\ x/
$$\frac{1}{\operatorname{asec}{\left(1 \cdot \frac{1}{x} \right)}}$$
d / 1 \ --|---------| dx| / 1\| |asec|1*-|| \ \ x//
$$\frac{d}{d x} \frac{1}{\operatorname{asec}{\left(1 \cdot \frac{1}{x} \right)}}$$
The first derivative
[src]
1
----------------------
________
/ 2 2/ 1\
\/ 1 - x *asec |1*-|
\ x/
$$\frac{1}{\sqrt{- x^{2} + 1} \operatorname{asec}^{2}{\left(1 \cdot \frac{1}{x} \right)}}$$
The second derivative
[src]
x 2
----------- - -----------------
3/2 / 2\ /1\
/ 2\ \-1 + x /*asec|-|
\1 - x / \x/
-------------------------------
2/1\
asec |-|
\x/
$$\frac{\frac{x}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{asec}{\left(\frac{1}{x} \right)}}}{\operatorname{asec}^{2}{\left(\frac{1}{x} \right)}}$$
The third derivative
[src]
2
1 3*x 6 6*x
----------- + ----------- + -------------------- + ------------------
3/2 5/2 3/2 2
/ 2\ / 2\ / 2\ 2/1\ / 2\ /1\
\1 - x / \1 - x / \1 - x / *asec |-| \-1 + x / *asec|-|
\x/ \x/
---------------------------------------------------------------------
2/1\
asec |-|
\x/
$$\frac{\frac{6 x}{\left(x^{2} - 1\right)^{2} \operatorname{asec}{\left(\frac{1}{x} \right)}} + \frac{3 x^{2}}{\left(- x^{2} + 1\right)^{\frac{5}{2}}} + \frac{1}{\left(- x^{2} + 1\right)^{\frac{3}{2}}} + \frac{6}{\left(- x^{2} + 1\right)^{\frac{3}{2}} \operatorname{asec}^{2}{\left(\frac{1}{x} \right)}}}{\operatorname{asec}^{2}{\left(\frac{1}{x} \right)}}$$