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Derivada de:
Derivada de x^-4/5
Derivada de x^2*5^x
Derivada de x/(1+e^x)
Derivada de u/v
Ecuación diferencial:
y'
Expresiones idénticas
y'=√tan(x- cinco)cos²(x⁵)
y signo de prima para el primer (1) orden es igual a √ tangente de (x menos 5) coseno de ²(x⁵)
y signo de prima para el primer (1) orden es igual a √ tangente de (x menos cinco) coseno de ²(x⁵)
y'=√tanx-5cos²x⁵
Expresiones semejantes
y'=√tan(x+5)cos²(x⁵)

Derivada de la función/ y'=√tan(x-5)cos²(x⁵)

Derivada de y'=√tan(x-5)cos²(x⁵)

Solución

Ha introducido [src]

  ____________    2/ 5\
\/ tan(x - 5) *cos \x /

\cos^{2}{\left(x^{5} \right)} \sqrt{\tan{\left(x - 5 \right)}}

sqrt(tan(x - 5))*cos(x^5)^2

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

         /       2       \                                       
   2/ 5\ |1   tan (x - 5)|                                       
cos \x /*|- + -----------|                                       
         \2        2     /       4   ____________    / 5\    / 5\
-------------------------- - 10*x *\/ tan(x - 5) *cos\x /*sin\x /
        ____________                                             
      \/ tan(x - 5)

- 10 x^{4} \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)} \sqrt{\tan{\left(x - 5 \right)}} + \frac{\left(\frac{\tan^{2}{\left(x - 5 \right)}}{2} + \frac{1}{2}\right) \cos^{2}{\left(x^{5} \right)}}{\sqrt{\tan{\left(x - 5 \right)}}}

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Segunda derivada [src]

 /                                                                                                          /                             2        \                                           \
 |                                                                                 2/ 5\ /       2        \ |      _____________   1 + tan (-5 + x)|                                           |
 |                                                                              cos \x /*\1 + tan (-5 + x)/*|- 4*\/ tan(-5 + x)  + ----------------|                                           |
 |                                                                                                          |                          3/2         |       4 /       2        \    / 5\    / 5\|
 |    3   _____________ /     5    2/ 5\        / 5\    / 5\      5    2/ 5\\                               \                       tan   (-5 + x) /   10*x *\1 + tan (-5 + x)/*cos\x /*sin\x /|
-|10*x *\/ tan(-5 + x) *\- 5*x *sin \x / + 4*cos\x /*sin\x / + 5*x *cos \x // + -------------------------------------------------------------------- + ----------------------------------------|
 |                                                                                                               4                                                   _____________             |
 \                                                                                                                                                                 \/ tan(-5 + x)              /

- (\frac{10 x^{4} \left(\tan^{2}{\left(x - 5 \right)} + 1\right) \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}}{\sqrt{\tan{\left(x - 5 \right)}}} + 10 x^{3} \left(- 5 x^{5} \sin^{2}{\left(x^{5} \right)} + 5 x^{5} \cos^{2}{\left(x^{5} \right)} + 4 \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}\right) \sqrt{\tan{\left(x - 5 \right)}} + \frac{\left(\frac{\tan^{2}{\left(x - 5 \right)} + 1}{\tan^{\frac{3}{2}}{\left(x - 5 \right)}} - 4 \sqrt{\tan{\left(x - 5 \right)}}\right) \left(\tan^{2}{\left(x - 5 \right)} + 1\right) \cos^{2}{\left(x^{5} \right)}}{4})

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Tercera derivada [src]

                                                                                                                                     /                                                               2\                                                                                                                                                                     
                                                                                                                                     |                      /       2        \     /       2        \ |                                                                                                             /                             2        \                
                                                                                                            2/ 5\ /       2        \ |      3/2           4*\1 + tan (-5 + x)/   3*\1 + tan (-5 + x)/ |                                                                                        4 /       2        \ |      _____________   1 + tan (-5 + x)|    / 5\    / 5\
                                                                                                         cos \x /*\1 + tan (-5 + x)/*|16*tan   (-5 + x) - -------------------- + ---------------------|                                                                                    15*x *\1 + tan (-5 + x)/*|- 4*\/ tan(-5 + x)  + ----------------|*cos\x /*sin\x /
                                                                                                                                     |                        _____________             5/2           |       3 /       2        \ /     5    2/ 5\        / 5\    / 5\      5    2/ 5\\                            |                          3/2         |                
    2   _____________ /      5    2/ 5\        / 5\    / 5\       5    2/ 5\       10    / 5\    / 5\\                               \                      \/ tan(-5 + x)           tan   (-5 + x)   /   15*x *\1 + tan (-5 + x)/*\- 5*x *sin \x / + 4*cos\x /*sin\x / + 5*x *cos \x //                            \                       tan   (-5 + x) /                
40*x *\/ tan(-5 + x) *\- 15*x *cos \x / - 3*cos\x /*sin\x / + 15*x *sin \x / + 25*x  *cos\x /*sin\x // + ---------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------
                                                                                                                                                       8                                                                                   _____________                                                                           2                                        
                                                                                                                                                                                                                                         \/ tan(-5 + x)

\frac{15 x^{4} \left(\frac{\tan^{2}{\left(x - 5 \right)} + 1}{\tan^{\frac{3}{2}}{\left(x - 5 \right)}} - 4 \sqrt{\tan{\left(x - 5 \right)}}\right) \left(\tan^{2}{\left(x - 5 \right)} + 1\right) \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}}{2} - \frac{15 x^{3} \left(\tan^{2}{\left(x - 5 \right)} + 1\right) \left(- 5 x^{5} \sin^{2}{\left(x^{5} \right)} + 5 x^{5} \cos^{2}{\left(x^{5} \right)} + 4 \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}\right)}{\sqrt{\tan{\left(x - 5 \right)}}} + 40 x^{2} \left(25 x^{10} \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)} + 15 x^{5} \sin^{2}{\left(x^{5} \right)} - 15 x^{5} \cos^{2}{\left(x^{5} \right)} - 3 \sin{\left(x^{5} \right)} \cos{\left(x^{5} \right)}\right) \sqrt{\tan{\left(x - 5 \right)}} + \frac{\left(\tan^{2}{\left(x - 5 \right)} + 1\right) \left(\frac{3 \left(\tan^{2}{\left(x - 5 \right)} + 1\right)^{2}}{\tan^{\frac{5}{2}}{\left(x - 5 \right)}} - \frac{4 \left(\tan^{2}{\left(x - 5 \right)} + 1\right)}{\sqrt{\tan{\left(x - 5 \right)}}} + 16 \tan^{\frac{3}{2}}{\left(x - 5 \right)}\right) \cos^{2}{\left(x^{5} \right)}}{8}

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Gráfico

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Expresiones idénticas

Expresiones semejantes

Derivada de y'=√tan(x-5)cos²(x⁵)

Gráfico:

Definida a trozos:

Solución