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^3-4*x^2+3)^7
-
Derivative of (x^2)/(x^3+1)
-
Derivative of sin9x
-
Derivative of e^x*log(sin(x))
-
Identical expressions
- acos^ two (x/ two)
- arc co sinus of e of ine of squared (x divide by 2)
- arc co sinus of e of ine of to the power of two (x divide by two)
- acos2(x/2)
- acos2x/2
- acos²(x/2)
- acos to the power of 2(x/2)
- acos^2x/2
- acos^2(x divide by 2)
Derivative of acos^2(x/2)
The solution
You have entered
[src]
2/x\
acos |-|
\2/
$$\operatorname{acos}^{2}{\left(\frac{x}{2} \right)}$$
acos(x/2)^2
The first derivative
[src]
/x\
-acos|-|
\2/
-------------
________
/ 2
/ x
/ 1 - --
\/ 4
$$- \frac{\operatorname{acos}{\left(\frac{x}{2} \right)}}{\sqrt{1 - \frac{x^{2}}{4}}}$$
The second derivative
[src]
/x\
x*acos|-|
2 \2/
- ------- - -------------
2 3/2
-4 + x / 2\
| x |
4*|1 - --|
\ 4 /
$$- \frac{x \operatorname{acos}{\left(\frac{x}{2} \right)}}{4 \left(1 - \frac{x^{2}}{4}\right)^{\frac{3}{2}}} - \frac{2}{x^{2} - 4}$$
The third derivative
[src]
/x\ 2 /x\
acos|-| 3*x *acos|-|
6*x \2/ \2/
---------- - ------------- - --------------
2 3/2 5/2
/ 2\ / 2\ / 2\
\-4 + x / | x | | x |
4*|1 - --| 16*|1 - --|
\ 4 / \ 4 /
$$- \frac{3 x^{2} \operatorname{acos}{\left(\frac{x}{2} \right)}}{16 \left(1 - \frac{x^{2}}{4}\right)^{\frac{5}{2}}} + \frac{6 x}{\left(x^{2} - 4\right)^{2}} - \frac{\operatorname{acos}{\left(\frac{x}{2} \right)}}{4 \left(1 - \frac{x^{2}}{4}\right)^{\frac{3}{2}}}$$