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
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How to use it?
- Derivative of:
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Derivative of cos(x/3)
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Derivative of √x
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Derivative of xcos(x)
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Derivative of x^4-1/5*cos(x)^(5)+2
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Identical expressions
- cos(asin(x)/ two)
- co sinus of e of ( arc sinus of e of (x) divide by 2)
- co sinus of e of ( arc sinus of e of (x) divide by two)
- cosasinx/2
- cos(asin(x) divide by 2)
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Similar expressions
- cos(arcsin(x)/2)
- cos(arcsinx/2)
Derivative of cos(asin(x)/2)
The solution
You have entered
[src]
/asin(x)\ cos|-------| \ 2 /
$$\cos{\left(\frac{\operatorname{asin}{\left(x \right)}}{2} \right)}$$
cos(asin(x)/2)
The first derivative
[src]
/asin(x)\
-sin|-------|
\ 2 /
--------------
________
/ 2
2*\/ 1 - x
$$- \frac{\sin{\left(\frac{\operatorname{asin}{\left(x \right)}}{2} \right)}}{2 \sqrt{1 - x^{2}}}$$
The second derivative
[src]
/asin(x)\ /asin(x)\
cos|-------| 2*x*sin|-------|
\ 2 / \ 2 /
------------ - ----------------
2 3/2
-1 + x / 2\
\1 - x /
-------------------------------
4
$$\frac{- \frac{2 x \sin{\left(\frac{\operatorname{asin}{\left(x \right)}}{2} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\cos{\left(\frac{\operatorname{asin}{\left(x \right)}}{2} \right)}}{x^{2} - 1}}{4}$$
The third derivative
[src]
/ /asin(x)\ /asin(x)\ 2 /asin(x)\\
|sin|-------| 2*x*cos|-------| 4*x *sin|-------||
| \ 2 / \ 2 / \ 2 /|
-3*|------------ + ---------------- + -----------------|
| 3/2 2 5/2 |
|/ 2\ / 2\ / 2\ |
\\1 - x / \-1 + x / \1 - x / /
--------------------------------------------------------
8
$$- \frac{3 \left(\frac{4 x^{2} \sin{\left(\frac{\operatorname{asin}{\left(x \right)}}{2} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{2 x \cos{\left(\frac{\operatorname{asin}{\left(x \right)}}{2} \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{\sin{\left(\frac{\operatorname{asin}{\left(x \right)}}{2} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)}{8}$$