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y=(cos(3x^5))/(√arctg4x)
Derivada de la función/ ctg4x/ arctg/ y=(cos(3x^5))/(√arctg4x)

Derivada de y=(cos(3x^5))/(√arctg4x)

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

Ha introducido [src] 
     /   5\  
  cos\3*x /  
-------------
  ___________
\/ atan(4*x)
cos⁡(3x5)atan⁡(4x)\frac{\cos{\left(3 x^{5} \right)}}{\sqrt{\operatorname{atan}{\left(4 x \right)}}} 
cos(3*x^5)/sqrt(atan(4*x))
Gráfica
02468-8-6-4-2-1010-200000200000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      4    /   5\              /   5\       
  15*x *sin\3*x /         2*cos\3*x /       
- --------------- - ------------------------
     ___________    /        2\     3/2     
   \/ atan(4*x)     \1 + 16*x /*atan   (4*x)
−15x4sin⁡(3x5)atan⁡(4x)−2cos⁡(3x5)(16x2+1)atan⁡32(4x)- \frac{15 x^{4} \sin{\left(3 x^{5} \right)}}{\sqrt{\operatorname{atan}{\left(4 x \right)}}} - \frac{2 \cos{\left(3 x^{5} \right)}}{\left(16 x^{2} + 1\right) \operatorname{atan}^{\frac{3}{2}}{\left(4 x \right)}}
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Segunda derivada [src] 
                                            /    3           \    /   5\                        
                                          4*|--------- + 16*x|*cos\3*x /          4    /   5\   
      3 /     /   5\       5    /   5\\     \atan(4*x)       /                60*x *sin\3*x /   
- 15*x *\4*sin\3*x / + 15*x *cos\3*x // + ------------------------------ + ---------------------
                                                         2                 /        2\          
                                              /        2\                  \1 + 16*x /*atan(4*x)
                                              \1 + 16*x / *atan(4*x)                            
------------------------------------------------------------------------------------------------
                                           ___________                                          
                                         \/ atan(4*x)
60x4sin⁡(3x5)(16x2+1)atan⁡(4x)−15x3(15x5cos⁡(3x5)+4sin⁡(3x5))+4(16x+3atan⁡(4x))cos⁡(3x5)(16x2+1)2atan⁡(4x)atan⁡(4x)\frac{\frac{60 x^{4} \sin{\left(3 x^{5} \right)}}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - 15 x^{3} \left(15 x^{5} \cos{\left(3 x^{5} \right)} + 4 \sin{\left(3 x^{5} \right)}\right) + \frac{4 \left(16 x + \frac{3}{\operatorname{atan}{\left(4 x \right)}}\right) \cos{\left(3 x^{5} \right)}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}}}{\sqrt{\operatorname{atan}{\left(4 x \right)}}}
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Tercera derivada [src] 
                                                               /                                     2                         \                                                                                        
                                                               |               15               512*x             144*x        |    /   5\                                                                              
                                                             8*|-8 + ---------------------- + --------- + ---------------------|*cos\3*x /                                                4 /    3           \    /   5\
                                                               |     /        2\     2                2   /        2\          |                 3 /     /   5\       5    /   5\\   180*x *|--------- + 16*x|*sin\3*x /
      2 /     /   5\       10    /   5\       5    /   5\\     \     \1 + 16*x /*atan (4*x)   1 + 16*x    \1 + 16*x /*atan(4*x)/             90*x *\4*sin\3*x / + 15*x *cos\3*x //          \atan(4*x)       /          
- 45*x *\4*sin\3*x / - 75*x  *sin\3*x / + 60*x *cos\3*x // - ----------------------------------------------------------------------------- + ------------------------------------- - -----------------------------------
                                                                                                    2                                                /        2\                                       2                
                                                                                         /        2\                                                 \1 + 16*x /*atan(4*x)                  /        2\                 
                                                                                         \1 + 16*x / *atan(4*x)                                                                             \1 + 16*x / *atan(4*x)      
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                       ___________                                                                                                      
                                                                                                     \/ atan(4*x)
−180x4(16x+3atan⁡(4x))sin⁡(3x5)(16x2+1)2atan⁡(4x)+90x3(15x5cos⁡(3x5)+4sin⁡(3x5))(16x2+1)atan⁡(4x)−45x2(−75x10sin⁡(3x5)+60x5cos⁡(3x5)+4sin⁡(3x5))−8(512x216x2+1+144x(16x2+1)atan⁡(4x)−8+15(16x2+1)atan⁡2(4x))cos⁡(3x5)(16x2+1)2atan⁡(4x)atan⁡(4x)\frac{- \frac{180 x^{4} \left(16 x + \frac{3}{\operatorname{atan}{\left(4 x \right)}}\right) \sin{\left(3 x^{5} \right)}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + \frac{90 x^{3} \left(15 x^{5} \cos{\left(3 x^{5} \right)} + 4 \sin{\left(3 x^{5} \right)}\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - 45 x^{2} \left(- 75 x^{10} \sin{\left(3 x^{5} \right)} + 60 x^{5} \cos{\left(3 x^{5} \right)} + 4 \sin{\left(3 x^{5} \right)}\right) - \frac{8 \left(\frac{512 x^{2}}{16 x^{2} + 1} + \frac{144 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - 8 + \frac{15}{\left(16 x^{2} + 1\right) \operatorname{atan}^{2}{\left(4 x \right)}}\right) \cos{\left(3 x^{5} \right)}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}}}{\sqrt{\operatorname{atan}{\left(4 x \right)}}}
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Gráfico
Derivada de y=(cos(3x^5))/(√arctg4x)
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