Mister Exam

Other calculators

The derivative of the function/ (7/x^2)-arcsin(x+2)

Derivative of (7/x^2)-arcsin(x+2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
7               
-- - asin(x + 2)
 2              
x
−asin⁡(x+2)+7x2- \operatorname{asin}{\left(x + 2 \right)} + \frac{7}{x^{2}} 
d /7               \
--|-- - asin(x + 2)|
dx| 2              |
  \x               /
ddx(−asin⁡(x+2)+7x2)\frac{d}{d x} \left(- \operatorname{asin}{\left(x + 2 \right)} + \frac{7}{x^{2}}\right)
Transform
The first derivative [src] 
          1           14
- ----------------- - --
     ______________    3
    /            2    x 
  \/  1 - (x + 2)
−11−(x+2)2−14x3- \frac{1}{\sqrt{1 - \left(x + 2\right)^{2}}} - \frac{14}{x^{3}}
Simplify
The second derivative [src] 
42         2 + x      
-- - -----------------
 4                 3/2
x    /           2\   
     \1 - (2 + x) /
−x+2(1−(x+2)2)32+42x4- \frac{x + 2}{\left(1 - \left(x + 2\right)^{2}\right)^{\frac{3}{2}}} + \frac{42}{x^{4}}
Simplify
The third derivative [src] 
 /                                       2   \
 |        1           168       3*(2 + x)    |
-|----------------- + --- + -----------------|
 |              3/2     5                 5/2|
 |/           2\       x    /           2\   |
 \\1 - (2 + x) /            \1 - (2 + x) /   /
−(1(1−(x+2)2)32+3(x+2)2(1−(x+2)2)52+168x5)- (\frac{1}{\left(1 - \left(x + 2\right)^{2}\right)^{\frac{3}{2}}} + \frac{3 \left(x + 2\right)^{2}}{\left(1 - \left(x + 2\right)^{2}\right)^{\frac{5}{2}}} + \frac{168}{x^{5}})
Simplify
3-я производная [src] 
 /                                       2   \
 |        1           168       3*(2 + x)    |
-|----------------- + --- + -----------------|
 |              3/2     5                 5/2|
 |/           2\       x    /           2\   |
 \\1 - (2 + x) /            \1 - (2 + x) /   /
−(1(1−(x+2)2)32+3(x+2)2(1−(x+2)2)52+168x5)- (\frac{1}{\left(1 - \left(x + 2\right)^{2}\right)^{\frac{3}{2}}} + \frac{3 \left(x + 2\right)^{2}}{\left(1 - \left(x + 2\right)^{2}\right)^{\frac{5}{2}}} + \frac{168}{x^{5}})
Simplify
    © Mister Exam – Calculator