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:
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Derivada de e^(x/2)
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Derivada de x^3*log(x)
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Derivada de (x)^(1/2)
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Derivada de x*e
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Expresiones idénticas
- y=ln^2sinx/(lncosx)
- y es igual a ln al cuadrado seno de x dividir por (ln coseno de x)
- y=ln2sinx/(lncosx)
- y=ln2sinx/lncosx
- y=ln²sinx/(lncosx)
- y=ln en el grado 2sinx/(lncosx)
- y=ln^2sinx/lncosx
- y=ln^2sinx dividir por (lncosx)
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Expresiones con funciones
- ln
- ln(x+3)^3
- ln(x-1)
- ln(-x)
- ln(x^2-2x)
- ln(1+e^x)
Derivada de y=ln^2sinx/(lncosx)
Solución
Ha introducido
[src]
2 log (x)*sin(x) -------------- log(x)*cos(x)
$$\frac{\log{\left(x \right)}^{2} \sin{\left(x \right)}}{\log{\left(x \right)} \cos{\left(x \right)}}$$
(log(x)^2*sin(x))/((log(x)*cos(x)))
Solución detallada
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Se aplica la regla de la derivada parcial:
y .
Para calcular :
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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Sustituimos .
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Según el principio, aplicamos: tenemos
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Luego se aplica una cadena de reglas. Multiplicamos por :
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Derivado es .
Como resultado de la secuencia de reglas:
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; calculamos :
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La derivada del seno es igual al coseno:
Como resultado de:
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Para calcular :
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Se aplica la regla de la derivada de una multiplicación:
; calculamos :
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La derivada del coseno es igual a menos el seno:
; calculamos :
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Derivado es .
Como resultado de:
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Ahora aplicamos la regla de la derivada de una divesión:
Simplificamos:
Respuesta:
Primera derivada
[src]
/ cos(x)\
|log(x)*sin(x) - ------|*sin(x)
1 / 2 2*log(x)*sin(x)\ \ x /
-------------*|log (x)*cos(x) + ---------------| + -------------------------------
cos(x)*log(x) \ x / 2
cos (x)
$$\frac{\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \frac{1}{\log{\left(x \right)} \cos{\left(x \right)}} \left(\log{\left(x \right)}^{2} \cos{\left(x \right)} + \frac{2 \log{\left(x \right)} \sin{\left(x \right)}}{x}\right)$$
Segunda derivada
[src]
/ / cos(x)\ cos(x)\
| |log(x)*sin(x) - ------|*sin(x) log(x)*sin(x) - ------|
2 4*cos(x)*log(x) 2*(-1 + log(x))*sin(x) |cos(x) /sin(x) 1 \ / cos(x)\ 2*sin(x) \ x / x |
log (x)*sin(x) - --------------- + ---------------------- |------ + |------ - --------|*|log(x)*sin(x) - ------| + cos(x)*log(x) + -------- + ------------------------------- - ----------------------|*sin(x) / 2*sin(x)\ / cos(x)\
x 2 | 2 \cos(x) x*log(x)/ \ x / x cos(x) x*log(x) | 2*|cos(x)*log(x) + --------|*|log(x)*sin(x) - ------|
x \ x / \ x / \ x /
- --------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------
log(x) cos(x) cos(x)*log(x)
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
cos(x)
$$\frac{\frac{2 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x}\right)}{\log{\left(x \right)} \cos{\left(x \right)}} - \frac{\log{\left(x \right)}^{2} \sin{\left(x \right)} - \frac{4 \log{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{2 \left(\log{\left(x \right)} - 1\right) \sin{\left(x \right)}}{x^{2}}}{\log{\left(x \right)}} + \frac{\left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) + \frac{\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \log{\left(x \right)} \cos{\left(x \right)} - \frac{\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}}{x \log{\left(x \right)}} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}}}{\cos{\left(x \right)}}$$
Tercera derivada
[src]
/ /cos(x) 2*sin(x)\ /cos(x) 2*sin(x)\ \
| cos(x) 3*|------ + cos(x)*log(x) + --------| / cos(x)\ 3*|------ + cos(x)*log(x) + --------|*sin(x) 2 / cos(x)\ /sin(x) 1 \ / cos(x)\ /sin(x) 1 \ / cos(x)\ / cos(x)\ | / / cos(x)\ cos(x)\
| / 2 \ log(x)*sin(x) - ------ | 2 x | 3*|log(x)*sin(x) - ------| | 2 x | 3*sin (x)*|log(x)*sin(x) - ------| |------ - --------|*|log(x)*sin(x) - ------|*sin(x) |------ - --------|*|log(x)*sin(x) - ------| 4*|log(x)*sin(x) - ------|*sin(x)| | |log(x)*sin(x) - ------|*sin(x) log(x)*sin(x) - ------|
2 2*(-3 + 2*log(x))*sin(x) 6*log(x)*sin(x) 6*(-1 + log(x))*cos(x) |/sin(x) 1 \ /cos(x) 2*sin(x)\ / cos(x)\ | 1 2 2*sin (x) 2*sin(x) | 3*sin(x) 2*cos(x) 2*cos(x) x \ x / \ x / \ x / \ x / \cos(x) x*log(x)/ \ x / \cos(x) x*log(x)/ \ x / \ x / | / cos(x)\ / 2 4*cos(x)*log(x) 2*(-1 + log(x))*sin(x)\ / 2*sin(x)\ |cos(x) /sin(x) 1 \ / cos(x)\ 2*sin(x) \ x / x |
log (x)*cos(x) - ------------------------ + --------------- + ---------------------- ||------ - --------|*|------ + cos(x)*log(x) + --------| + |log(x)*sin(x) - ------|*|1 + --------- + ---------- + --------- - ---------------| - -------- - -------- + -------- + ---------------------- - ------------------------------------- + -------------------------- + -------------------------------------------- + ---------------------------------- + --------------------------------------------------- - -------------------------------------------- - ---------------------------------|*sin(x) 3*|log(x)*sin(x) - ------|*|log (x)*sin(x) - --------------- + ----------------------| 3*|cos(x)*log(x) + --------|*|------ + |------ - --------|*|log(x)*sin(x) - ------| + cos(x)*log(x) + -------- + ------------------------------- - ----------------------|
3 x 2 |\cos(x) x*log(x)/ | 2 x | \ x / | 2 2 2 2 x*cos(x)*log(x)| 2 3 x 2 x*log(x) 2 2 cos(x) 2 cos(x) x*log(x) x*cos(x)*log(x) | \ x / | x 2 | \ x / | 2 \cos(x) x*log(x)/ \ x / x cos(x) x*log(x) |
x x \ \ x / \ x *log(x) x *log (x) cos (x) / x x x *log(x) x *log (x) cos (x) / \ x / \ x /
- ------------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(x) cos(x) 2 cos(x)*log(x)
cos(x)*log (x)
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
cos(x)
$$\frac{- \frac{3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\log{\left(x \right)}^{2} \sin{\left(x \right)} - \frac{4 \log{\left(x \right)} \cos{\left(x \right)}}{x} + \frac{2 \left(\log{\left(x \right)} - 1\right) \sin{\left(x \right)}}{x^{2}}\right)}{\log{\left(x \right)}^{2} \cos{\left(x \right)}} + \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x}\right) \left(\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) + \frac{\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \log{\left(x \right)} \cos{\left(x \right)} - \frac{\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}}{x \log{\left(x \right)}} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right)}{\log{\left(x \right)} \cos{\left(x \right)}} - \frac{\log{\left(x \right)}^{2} \cos{\left(x \right)} + \frac{6 \log{\left(x \right)} \sin{\left(x \right)}}{x} + \frac{6 \left(\log{\left(x \right)} - 1\right) \cos{\left(x \right)}}{x^{2}} - \frac{2 \left(2 \log{\left(x \right)} - 3\right) \sin{\left(x \right)}}{x^{3}}}{\log{\left(x \right)}} + \frac{\left(\frac{\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - \frac{2 \sin{\left(x \right)}}{x \log{\left(x \right)} \cos{\left(x \right)}} + \frac{1}{x^{2} \log{\left(x \right)}} + \frac{2}{x^{2} \log{\left(x \right)}^{2}}\right) + \frac{3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right) \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) + \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{1}{x \log{\left(x \right)}}\right)}{x \log{\left(x \right)}} - \frac{4 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right) \sin{\left(x \right)}}{x \log{\left(x \right)} \cos{\left(x \right)}} - \frac{3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x} + \frac{\cos{\left(x \right)}}{x^{2}}\right)}{x \log{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{x} + \frac{\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}}{x^{2} \log{\left(x \right)}} + \frac{3 \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{\cos{\left(x \right)}}{x}\right)}{x^{2} \log{\left(x \right)}^{2}} - \frac{3 \sin{\left(x \right)}}{x^{2}} - \frac{2 \cos{\left(x \right)}}{x^{3}}\right) \sin{\left(x \right)}}{\cos{\left(x \right)}}}{\cos{\left(x \right)}}$$
Gráfico