Mister Exam

Other calculators

The derivative of the function/ asin((4x+3)/(x^2))

Derivative of asin((4x+3)/(x^2))

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    /4*x + 3\
asin|-------|
    |    2  |
    \   x   /
asin⁡(4x+3x2)\operatorname{asin}{\left(\frac{4 x + 3}{x^{2}} \right)} 
asin((4*x + 3)/x^2)
The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   4    2*(4*x + 3)   
   -- - -----------   
    2         3       
   x         x        
----------------------
      ________________
     /              2 
    /      (4*x + 3)  
   /   1 - ---------- 
  /             4     
\/             x
4x2−2(4x+3)x31−(4x+3)2x4\frac{\frac{4}{x^{2}} - \frac{2 \left(4 x + 3\right)}{x^{3}}}{\sqrt{1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}}}
Simplify
The second derivative [src] 
  /                                  2          \
  |                     /    3 + 4*x\           |
  |                   2*|2 - -------| *(3 + 4*x)|
  |     3*(3 + 4*x)     \       x   /           |
2*|-8 + ----------- + --------------------------|
  |          x              /             2\    |
  |                       3 |    (3 + 4*x) |    |
  |                      x *|1 - ----------|    |
  |                         |         4    |    |
  \                         \        x     /    /
-------------------------------------------------
                     ________________            
                    /              2             
             3     /      (3 + 4*x)              
            x *   /   1 - ----------             
                 /             4                 
               \/             x
2(−8+3(4x+3)x+2(2−4x+3x)2(4x+3)x3(1−(4x+3)2x4))x31−(4x+3)2x4\frac{2 \left(-8 + \frac{3 \left(4 x + 3\right)}{x} + \frac{2 \left(2 - \frac{4 x + 3}{x}\right)^{2} \left(4 x + 3\right)}{x^{3} \left(1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}\right)}\right)}{x^{3} \sqrt{1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}}}
Simplify
The third derivative [src] 
  /                                 /                              2\                                                                            \
  |                   /    3 + 4*x\ |    16*(3 + 4*x)   5*(3 + 4*x) |                  3                                                         |
  |                   |2 - -------|*|8 - ------------ + ------------|     /    3 + 4*x\           2     /    3 + 4*x\           /    3*(3 + 4*x)\|
  |                   \       x   / |         x               2     |   6*|2 - -------| *(3 + 4*x)    2*|2 - -------|*(3 + 4*x)*|8 - -----------||
  |     6*(3 + 4*x)                 \                        x      /     \       x   /                 \       x   /           \         x     /|
4*|18 - ----------- + ----------------------------------------------- + --------------------------- - -------------------------------------------|
  |          x                         /             2\                                        2                     /             2\            |
  |                                  2 |    (3 + 4*x) |                        /             2\                    3 |    (3 + 4*x) |            |
  |                                 x *|1 - ----------|                      6 |    (3 + 4*x) |                   x *|1 - ----------|            |
  |                                    |         4    |                     x *|1 - ----------|                      |         4    |            |
  |                                    \        x     /                        |         4    |                      \        x     /            |
  \                                                                            \        x     /                                                  /
--------------------------------------------------------------------------------------------------------------------------------------------------
                                                                     ________________                                                             
                                                                    /              2                                                              
                                                             4     /      (3 + 4*x)                                                               
                                                            x *   /   1 - ----------                                                              
                                                                 /             4                                                                  
                                                               \/             x
4(18−6(4x+3)x+(2−4x+3x)(8−16(4x+3)x+5(4x+3)2x2)x2(1−(4x+3)2x4)−2(2−4x+3x)(8−3(4x+3)x)(4x+3)x3(1−(4x+3)2x4)+6(2−4x+3x)3(4x+3)2x6(1−(4x+3)2x4)2)x41−(4x+3)2x4\frac{4 \left(18 - \frac{6 \left(4 x + 3\right)}{x} + \frac{\left(2 - \frac{4 x + 3}{x}\right) \left(8 - \frac{16 \left(4 x + 3\right)}{x} + \frac{5 \left(4 x + 3\right)^{2}}{x^{2}}\right)}{x^{2} \left(1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}\right)} - \frac{2 \left(2 - \frac{4 x + 3}{x}\right) \left(8 - \frac{3 \left(4 x + 3\right)}{x}\right) \left(4 x + 3\right)}{x^{3} \left(1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}\right)} + \frac{6 \left(2 - \frac{4 x + 3}{x}\right)^{3} \left(4 x + 3\right)^{2}}{x^{6} \left(1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}\right)^{2}}\right)}{x^{4} \sqrt{1 - \frac{\left(4 x + 3\right)^{2}}{x^{4}}}}
Simplify
    © Mister Exam – Calculator