Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
- Derivada de e^((3*x)^2)
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Derivada de d/dx(x)
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Derivada de (cos(x))^x^2
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Derivada de (8*x-15)^5
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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
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Expresiones semejantes
- y=(log10(x^3+x^2))^tg5x+sinpi/6
- 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
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diferenciamos miembro por miembro:
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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La derivada de una constante es igual a cero.
Como resultado de:
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Respuesta:
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 //
$$\left(\frac{\log{\left(x^{3} - x^{2} \right)}}{\log{\left(10 \right)}}\right)^{\tan{\left(5 x \right)}} \left(\frac{\left(3 x^{2} - 2 x\right) \tan{\left(5 x \right)}}{\left(x^{3} - x^{2}\right) \log{\left(x^{3} - x^{2} \right)}} + \left(5 \tan^{2}{\left(5 x \right)} + 5\right) \log{\left(\frac{\log{\left(x^{3} - x^{2} \right)}}{\log{\left(10 \right)}} \right)}\right)$$
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)/ /
$$\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}}\right)^{\tan{\left(5 x \right)}} \left(\left(5 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}} \right)} + \frac{\left(3 x - 2\right) \tan{\left(5 x \right)}}{x \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}}\right)^{2} + 50 \left(\tan^{2}{\left(5 x \right)} + 1\right) \log{\left(\frac{\log{\left(x^{2} \left(x - 1\right) \right)}}{\log{\left(10 \right)}} \right)} \tan{\left(5 x \right)} + \frac{10 \left(3 x - 2\right) \left(\tan^{2}{\left(5 x \right)} + 1\right)}{x \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}} + \frac{2 \left(3 x - 1\right) \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right) \log{\left(x^{2} \left(x - 1\right) \right)}} - \frac{\left(3 x - 2\right)^{2} \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}} - \frac{\left(3 x - 2\right)^{2} \tan{\left(5 x \right)}}{x^{2} \left(x - 1\right)^{2} \log{\left(x^{2} \left(x - 1\right) \right)}^{2}}\right)$$
Tercera derivada
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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)$$
Gráfico