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y=ln(tgx/sqrtx)
Derivada de la función/ sqrtx/ y=ln(tgx/sqrtx)

Derivada de y=ln(tgx/sqrtx)

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

Gráfico:

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Solución

Ha introducido [src] 
   /tan(x)\
log|------|
   |  ___ |
   \\/ x  /
log⁡(tan⁡(x)x)\log{\left(\frac{\tan{\left(x \right)}}{\sqrt{x}} \right)} 
log(tan(x)/sqrt(x))
Gráfica
02468-8-6-4-2-1010-200200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      /       2            \
  ___ |1 + tan (x)   tan(x)|
\/ x *|----------- - ------|
      |     ___         3/2|
      \   \/ x       2*x   /
----------------------------
           tan(x)
x(tan⁡2(x)+1x−tan⁡(x)2x32)tan⁡(x)\frac{\sqrt{x} \left(\frac{\tan^{2}{\left(x \right)} + 1}{\sqrt{x}} - \frac{\tan{\left(x \right)}}{2 x^{\frac{3}{2}}}\right)}{\tan{\left(x \right)}}
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Segunda derivada [src] 
                                                  2      tan(x)              /       2   \ /         2      tan(x)\
         2                               2 + 2*tan (x) - ------              \1 + tan (x)/*|2 + 2*tan (x) - ------|
  1 + tan (x)     /       2   \                            x      3*tan(x)                 \                  x   /
- ----------- + 2*\1 + tan (x)/*tan(x) + ---------------------- + -------- - --------------------------------------
       x                                          4*x                  2                    2*tan(x)               
                                                                    4*x                                            
-------------------------------------------------------------------------------------------------------------------
                                                       tan(x)
−(tan⁡2(x)+1)(2tan⁡2(x)+2−tan⁡(x)x)2tan⁡(x)+2(tan⁡2(x)+1)tan⁡(x)−tan⁡2(x)+1x+2tan⁡2(x)+2−tan⁡(x)x4x+3tan⁡(x)4x2tan⁡(x)\frac{- \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(2 \tan^{2}{\left(x \right)} + 2 - \frac{\tan{\left(x \right)}}{x}\right)}{2 \tan{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{2 \tan^{2}{\left(x \right)} + 2 - \frac{\tan{\left(x \right)}}{x}}{4 x} + \frac{3 \tan{\left(x \right)}}{4 x^{2}}}{\tan{\left(x \right)}}
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Tercera derivada [src] 
                                                                                                                               /       2   \                                                                                                                                          /    /       2   \                                    \                                         
                                                                                                                             4*\1 + tan (x)/   3*tan(x)     /       2   \                                         2                                                     /       2   \ |  4*\1 + tan (x)/   3*tan(x)     /       2   \       |                                         
                                                                                                           2      tan(x)   - --------------- + -------- + 8*\1 + tan (x)/*tan(x)                     /       2   \  /         2      tan(x)\                            \1 + tan (x)/*|- --------------- + -------- + 8*\1 + tan (x)/*tan(x)|   /       2   \ /         2      tan(x)\
               2                                                                                  2 + 2*tan (x) - ------            x              2                                 /       2   \   \1 + tan (x)/ *|2 + 2*tan (x) - ------|     /       2   \                        |         x              2                            |   \1 + tan (x)/*|2 + 2*tan (x) - ------|
  /       2   \    /       2   \ /         2      tan(x)\        2    /       2   \   15*tan(x)                     x                             x                                9*\1 + tan (x)/                  \                  x   /   3*\1 + tan (x)/*tan(x)                 \                       x                             /                 \                  x   /
2*\1 + tan (x)/  - \1 + tan (x)/*|2 + 2*tan (x) - ------| + 4*tan (x)*\1 + tan (x)/ - --------- - ---------------------- + ----------------------------------------------------- + --------------- + --------------------------------------- - ---------------------- - --------------------------------------------------------------------- - --------------------------------------
                                 \                  x   /                                   3                 2                                     4*x                                     2                           2                                x                                             2*tan(x)                                               2*x*tan(x)              
                                                                                         8*x               8*x                                                                           4*x                         tan (x)                                                                                                                                                          
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                        tan(x)
(tan⁡2(x)+1)2(2tan⁡2(x)+2−tan⁡(x)x)tan⁡2(x)+2(tan⁡2(x)+1)2−(tan⁡2(x)+1)(8(tan⁡2(x)+1)tan⁡(x)−4(tan⁡2(x)+1)x+3tan⁡(x)x2)2tan⁡(x)−(tan⁡2(x)+1)(2tan⁡2(x)+2−tan⁡(x)x)+4(tan⁡2(x)+1)tan⁡2(x)−(tan⁡2(x)+1)(2tan⁡2(x)+2−tan⁡(x)x)2xtan⁡(x)−3(tan⁡2(x)+1)tan⁡(x)x+8(tan⁡2(x)+1)tan⁡(x)−4(tan⁡2(x)+1)x+3tan⁡(x)x24x+9(tan⁡2(x)+1)4x2−2tan⁡2(x)+2−tan⁡(x)x8x2−15tan⁡(x)8x3tan⁡(x)\frac{\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \left(2 \tan^{2}{\left(x \right)} + 2 - \frac{\tan{\left(x \right)}}{x}\right)}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{3 \tan{\left(x \right)}}{x^{2}}\right)}{2 \tan{\left(x \right)}} - \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 \tan^{2}{\left(x \right)} + 2 - \frac{\tan{\left(x \right)}}{x}\right) + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(2 \tan^{2}{\left(x \right)} + 2 - \frac{\tan{\left(x \right)}}{x}\right)}{2 x \tan{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} + \frac{8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{3 \tan{\left(x \right)}}{x^{2}}}{4 x} + \frac{9 \left(\tan^{2}{\left(x \right)} + 1\right)}{4 x^{2}} - \frac{2 \tan^{2}{\left(x \right)} + 2 - \frac{\tan{\left(x \right)}}{x}}{8 x^{2}} - \frac{15 \tan{\left(x \right)}}{8 x^{3}}}{\tan{\left(x \right)}}
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Gráfico
Derivada de y=ln(tgx/sqrtx)
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