Sr Examen

Otras calculadoras

Derivada de la función/ (x^2)/ y=cos/ cos^2/ x/(sqrt(x^2)+1)/ y=cos^2x/(sqrt(x^2)+1)

Derivada de y=cos^2x/(sqrt(x^2)+1)

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     2     
  cos (x)  
-----------
   ____    
  /  2     
\/  x   + 1
cos⁡2(x)x2+1\frac{\cos^{2}{\left(x \right)}}{\sqrt{x^{2}} + 1} 
cos(x)^2/(sqrt(x^2) + 1)
Primera derivada [src] 
                         2          
  2*cos(x)*sin(x)     cos (x)*|x|   
- --------------- - ----------------
       ____                        2
      /  2            /   ____    \ 
    \/  x   + 1       |  /  2     | 
                    x*\\/  x   + 1/
−2sin⁡(x)cos⁡(x)x2+1−cos⁡2(x)∣x∣x(x2+1)2- \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{x^{2}} + 1} - \frac{\cos^{2}{\left(x \right)} \left|{x}\right|}{x \left(\sqrt{x^{2}} + 1\right)^{2}}
Simplificar
Segunda derivada [src] 
                             2    /   2      |x|   sign(x)\                      
                          cos (x)*|------- + --- - -------|                      
                                  |1 + |x|     2      x   |                      
       2           2              \           x           /   4*|x|*cos(x)*sin(x)
- 2*cos (x) + 2*sin (x) + --------------------------------- + -------------------
                                       1 + |x|                    x*(1 + |x|)    
---------------------------------------------------------------------------------
                                     1 + |x|
2sin⁡2(x)−2cos⁡2(x)+(2∣x∣+1−sign⁡(x)x+∣x∣x2)cos⁡2(x)∣x∣+1+4sin⁡(x)cos⁡(x)∣x∣x(∣x∣+1)∣x∣+1\frac{2 \sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)} + \frac{\left(\frac{2}{\left|{x}\right| + 1} - \frac{\operatorname{sign}{\left(x \right)}}{x} + \frac{\left|{x}\right|}{x^{2}}\right) \cos^{2}{\left(x \right)}}{\left|{x}\right| + 1} + \frac{4 \sin{\left(x \right)} \cos{\left(x \right)} \left|{x}\right|}{x \left(\left|{x}\right| + 1\right)}}{\left|{x}\right| + 1}
Simplificar
Tercera derivada [src] 
  /                     2    /   1      |x|   sign(x)     3*|x|      |x|*sign(x)                \                                 /   2      |x|   sign(x)\              \
  |                  cos (x)*|------- + --- - ------- + ---------- - ----------- + DiracDelta(x)|                               3*|------- + --- - -------|*cos(x)*sin(x)|
  |                          |1 + |x|     2      x               2   x*(1 + |x|)                |     /   2         2   \         |1 + |x|     2      x   |              |
  |                          \           x              (1 + |x|)                               /   3*\sin (x) - cos (x)/*|x|     \           x           /              |
2*|4*cos(x)*sin(x) - ---------------------------------------------------------------------------- - ------------------------- - -----------------------------------------|
  \                                                  x*(1 + |x|)                                           x*(1 + |x|)                           1 + |x|                 /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                 1 + |x|
2(4sin⁡(x)cos⁡(x)−3(2∣x∣+1−sign⁡(x)x+∣x∣x2)sin⁡(x)cos⁡(x)∣x∣+1−3(sin⁡2(x)−cos⁡2(x))∣x∣x(∣x∣+1)−(δ(x)+1∣x∣+1+3∣x∣(∣x∣+1)2−sign⁡(x)x−∣x∣sign⁡(x)x(∣x∣+1)+∣x∣x2)cos⁡2(x)x(∣x∣+1))∣x∣+1\frac{2 \left(4 \sin{\left(x \right)} \cos{\left(x \right)} - \frac{3 \left(\frac{2}{\left|{x}\right| + 1} - \frac{\operatorname{sign}{\left(x \right)}}{x} + \frac{\left|{x}\right|}{x^{2}}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\left|{x}\right| + 1} - \frac{3 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \left|{x}\right|}{x \left(\left|{x}\right| + 1\right)} - \frac{\left(\delta\left(x\right) + \frac{1}{\left|{x}\right| + 1} + \frac{3 \left|{x}\right|}{\left(\left|{x}\right| + 1\right)^{2}} - \frac{\operatorname{sign}{\left(x \right)}}{x} - \frac{\left|{x}\right| \operatorname{sign}{\left(x \right)}}{x \left(\left|{x}\right| + 1\right)} + \frac{\left|{x}\right|}{x^{2}}\right) \cos^{2}{\left(x \right)}}{x \left(\left|{x}\right| + 1\right)}\right)}{\left|{x}\right| + 1}
Simplificar
    © Sr Examen – Калькулятор