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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
Expresiones idénticas
y=(log10(x^ tres -x^ dos))^tg5x+sinpi/ seis
y es igual a ( logaritmo de 10(x al cubo menos x al cuadrado )) en el grado tg5x más seno de número pi dividir por 6
y es igual a ( logaritmo de 10(x en el grado tres menos x en el grado dos)) en el grado tg5x más seno de número pi dividir por seis
y=(log10(x3-x2))tg5x+sinpi/6
y=log10x3-x2tg5x+sinpi/6
y=(log10(x³-x²))^tg5x+sinpi/6
y=(log10(x en el grado 3-x en el grado 2)) en el grado tg5x+sinpi/6
y=log10x^3-x^2^tg5x+sinpi/6
y=(log10(x^3-x^2))^tg5x+sinpi dividir por 6
Expresiones semejantes
y=(log10(x^3-x^2))^tg5x-sinpi/6
y=(log10(x^3+x^2))^tg5x+sinpi/6

Derivada de la función/ y=(log10(x^3-x^2))^tg5x+sinpi/6

Derivada de y=(log10(x^3-x^2))^tg5x+sinpi/6

Solución

Ha introducido [src]

              tan(5*x)          
/   / 3    2\\                  
|log\x  - x /|           sin(pi)
|------------|         + -------
\  log(10)   /              6

\left(\frac{\log{\left(x^{3} - x^{2} \right)}}{\log{\left(10 \right)}}\right)^{\tan{\left(5 x \right)}} + \frac{\sin{\left(\pi \right)}}{6}

(log(x^3 - x^2)/log(10))^tan(5*x) + sin(pi)/6

Solución detallada

diferenciamos $\left(\frac{\log{\left(x^{3} - x^{2} \right)}}{\log{\left(10 \right)}}\right)^{\tan{\left(5 x \right)}} + \frac{\sin{\left(\pi \right)}}{6}$ miembro por miembro:
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $\left(\log{\left(\tan{\left(5 x \right)} \right)} + 1\right) \tan^{\tan{\left(5 x \right)}}{\left(5 x \right)}$
2. La derivada de una constante $\frac{\sin{\left(\pi \right)}}{6}$ es igual a cero.
Como resultado de: $\left(\log{\left(\tan{\left(5 x \right)} \right)} + 1\right) \tan^{\tan{\left(5 x \right)}}{\left(5 x \right)}$

Respuesta:

$\left(\log{\left(\tan{\left(5 x \right)} \right)} + 1\right) \tan^{\tan{\left(5 x \right)}}{\left(5 x \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

              tan(5*x)                                                               
/   / 3    2\\         /                     /   / 3    2\\   /          2\         \
|log\x  - x /|         |/         2     \    |log\x  - x /|   \-2*x + 3*x /*tan(5*x)|
|------------|        *|\5 + 5*tan (5*x)/*log|------------| + ----------------------|
\  log(10)   /         |                     \  log(10)   /   / 3    2\    / 3    2\|
                       \                                      \x  - x /*log\x  - x //

\left(\frac{\log{\left(x^{3} - x^{2} \right)}}{\log{\left(10 \right)}}\right)^{\tan{\left(5 x \right)}} \left(\frac{\left(3 x^{2} - 2 x\right) \tan{\left(5 x \right)}}{\left(x^{3} - x^{2}\right) \log{\left(x^{3} - x^{2} \right)}} + \left(5 \tan^{2}{\left(5 x \right)} + 5\right) \log{\left(\frac{\log{\left(x^{3} - x^{2} \right)}}{\log{\left(10 \right)}} \right)}\right)

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Segunda derivada [src]

                  tan(5*x) /                                                                       2                                                                                                                                                                                    \
/   / 2         \\         |/                     /   / 2         \\                              \                          /   / 2         \\                           2                               2                                                   /       2     \           |
|log\x *(-1 + x)/|         ||  /       2     \    |log\x *(-1 + x)/|       (-2 + 3*x)*tan(5*x)    |       /       2     \    |log\x *(-1 + x)/|                 (-2 + 3*x) *tan(5*x)            (-2 + 3*x) *tan(5*x)           2*(-1 + 3*x)*tan(5*x)       10*\1 + tan (5*x)/*(-2 + 3*x)|
|----------------|        *||5*\1 + tan (5*x)/*log|----------------| + ---------------------------|  + 50*\1 + tan (5*x)/*log|----------------|*tan(5*x) - ----------------------------- - ------------------------------ + ---------------------------- + -----------------------------|
\    log(10)     /         ||                     \    log(10)     /                 / 2         \|                          \    log(10)     /             2         2    / 2         \    2         2    2/ 2         \    2             / 2         \                  / 2         \ |
                           \\                                          x*(-1 + x)*log\x *(-1 + x)//                                                        x *(-1 + x) *log\x *(-1 + x)/   x *(-1 + x) *log \x *(-1 + x)/   x *(-1 + x)*log\x *(-1 + x)/    x*(-1 + x)*log\x *(-1 + x)/ /

\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}}\right)^{\tan{\left(5 x \right)}} \left(\left(5 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}} \right)} + \frac{\left(3 x - 2\right) \tan{\left(5 x \right)}}{x \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}}\right)^{2} + 50 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}} \right)} \tan{\left(5 x \right)} + \frac{10 \left(3 x - 2\right) \left(\tan^{2}{\left(5 x \right)} + 1\right)}{x \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}} + \frac{2 \left(3 x - 1\right) \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}} - \frac{\left(3 x - 2\right)^{2} \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}} - \frac{\left(3 x - 2\right)^{2} \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}^{2}}\right)

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Tercera derivada [src]

                  tan(5*x) /                                                                       3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \
/   / 2         \\         |/                     /   / 2         \\                              \      /                     /   / 2         \\                              \ /                      /   / 2         \\                           2                               2                                                   /       2     \           \                      2    /   / 2         \\                                    /   / 2         \\                                               2 /       2     \                2 /       2     \                   3                               3                                3                   /       2     \                                                                                        /       2     \                    |
|log\x *(-1 + x)/|         ||  /       2     \    |log\x *(-1 + x)/|       (-2 + 3*x)*tan(5*x)    |      |  /       2     \    |log\x *(-1 + x)/|       (-2 + 3*x)*tan(5*x)    | |   /       2     \    |log\x *(-1 + x)/|                 (-2 + 3*x) *tan(5*x)            (-2 + 3*x) *tan(5*x)           2*(-1 + 3*x)*tan(5*x)       10*\1 + tan (5*x)/*(-2 + 3*x)|       /       2     \     |log\x *(-1 + x)/|          2      /       2     \    |log\x *(-1 + x)/|            6*tan(5*x)            15*(-2 + 3*x) *\1 + tan (5*x)/   15*(-2 + 3*x) *\1 + tan (5*x)/       2*(-2 + 3*x) *tan(5*x)          2*(-2 + 3*x) *tan(5*x)           3*(-2 + 3*x) *tan(5*x)       30*\1 + tan (5*x)/*(-1 + 3*x)   6*(-1 + 3*x)*(-2 + 3*x)*tan(5*x)   6*(-1 + 3*x)*(-2 + 3*x)*tan(5*x)   150*\1 + tan (5*x)/*(-2 + 3*x)*tan(5*x)|
|----------------|        *||5*\1 + tan (5*x)/*log|----------------| + ---------------------------|  + 3*|5*\1 + tan (5*x)/*log|----------------| + ---------------------------|*|50*\1 + tan (5*x)/*log|----------------|*tan(5*x) - ----------------------------- - ------------------------------ + ---------------------------- + -----------------------------| + 250*\1 + tan (5*x)/ *log|----------------| + 500*tan (5*x)*\1 + tan (5*x)/*log|----------------| + ---------------------------- - ------------------------------ - ------------------------------ + ----------------------------- + ------------------------------ + ------------------------------ + ----------------------------- - -------------------------------- - -------------------------------- + ---------------------------------------|
\    log(10)     /         ||                     \    log(10)     /                 / 2         \|      |                     \    log(10)     /                 / 2         \| |                      \    log(10)     /             2         2    / 2         \    2         2    2/ 2         \    2             / 2         \                  / 2         \ |                           \    log(10)     /                                    \    log(10)     /    2             / 2         \    2         2    / 2         \     2         2    2/ 2         \    3         3    / 2         \    3         3    3/ 2         \    3         3    2/ 2         \     2             / 2         \     3         2    / 2         \       3         2    2/ 2         \                        / 2         \      |
                           \\                                          x*(-1 + x)*log\x *(-1 + x)//      \                                          x*(-1 + x)*log\x *(-1 + x)// \                                                    x *(-1 + x) *log\x *(-1 + x)/   x *(-1 + x) *log \x *(-1 + x)/   x *(-1 + x)*log\x *(-1 + x)/    x*(-1 + x)*log\x *(-1 + x)/ /                                                                                                      x *(-1 + x)*log\x *(-1 + x)/   x *(-1 + x) *log\x *(-1 + x)/    x *(-1 + x) *log \x *(-1 + x)/   x *(-1 + x) *log\x *(-1 + x)/   x *(-1 + x) *log \x *(-1 + x)/   x *(-1 + x) *log \x *(-1 + x)/    x *(-1 + x)*log\x *(-1 + x)/    x *(-1 + x) *log\x *(-1 + x)/      x *(-1 + x) *log \x *(-1 + x)/          x*(-1 + x)*log\x *(-1 + x)/      /

\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}}\right)^{\tan{\left(5 x \right)}} \left(\left(5 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}} \right)} + \frac{\left(3 x - 2\right) \tan{\left(5 x \right)}}{x \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}}\right)^{3} + 3 \left(5 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}} \right)} + \frac{\left(3 x - 2\right) \tan{\left(5 x \right)}}{x \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}}\right) \left(50 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}} \right)} \tan{\left(5 x \right)} + \frac{10 \left(3 x - 2\right) \left(\tan^{2}{\left(5 x \right)} + 1\right)}{x \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}} + \frac{2 \left(3 x - 1\right) \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}} - \frac{\left(3 x - 2\right)^{2} \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}} - \frac{\left(3 x - 2\right)^{2} \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}^{2}}\right) + 250 \left(\tan^{2}{\left(5 x \right)} + 1\right)^{2} \log{\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}} \right)} + 500 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}} \right)} \tan^{2}{\left(5 x \right)} + \frac{150 \left(3 x - 2\right) \left(\tan^{2}{\left(5 x \right)} + 1\right) \tan{\left(5 x \right)}}{x \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}} + \frac{30 \left(3 x - 1\right) \left(\tan^{2}{\left(5 x \right)} + 1\right)}{x^{2} \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}} + \frac{6 \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}} - \frac{15 \left(3 x - 2\right)^{2} \left(\tan^{2}{\left(5 x \right)} + 1\right)}{x^{2} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}} - \frac{15 \left(3 x - 2\right)^{2} \left(\tan^{2}{\left(5 x \right)} + 1\right)}{x^{2} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}^{2}} - \frac{6 \left(3 x - 2\right) \left(3 x - 1\right) \tan{\left(5 x \right)}}{x^{3} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}} - \frac{6 \left(3 x - 2\right) \left(3 x - 1\right) \tan{\left(5 x \right)}}{x^{3} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}^{2}} + \frac{2 \left(3 x - 2\right)^{3} \tan{\left(5 x \right)}}{x^{3} \left(x - 1\right)^{3} \log{\left(x^{2} \left(x - 1\right) \right)}} + \frac{3 \left(3 x - 2\right)^{3} \tan{\left(5 x \right)}}{x^{3} \left(x - 1\right)^{3} \log{\left(x^{2} \left(x - 1\right) \right)}^{2}} + \frac{2 \left(3 x - 2\right)^{3} \tan{\left(5 x \right)}}{x^{3} \left(x - 1\right)^{3} \log{\left(x^{2} \left(x - 1\right) \right)}^{3}}\right)

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Gráfico

Derivada de y=(log10(x^3-x^2))^tg5x+sinpi/6

Otras calculadoras

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Expresiones idénticas

Expresiones semejantes

Derivada de y=(log10(x^3-x^2))^tg5x+sinpi/6

Gráfico:

Definida a trozos:

Solución