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 (π-2x)³
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Derivada de y=e×
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Derivada de y/(sqrt(5^2+y^2))
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Derivada de y=(3x-7)4
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Expresiones idénticas
- y=ln(sqrt((uno +sin5x)/(dos -cos3^x)))
- y es igual a ln( raíz cuadrada de ((1 más seno de 5x) dividir por (2 menos coseno de 3 en el grado x)))
- y es igual a ln( raíz cuadrada de ((uno más seno de 5x) dividir por (dos menos coseno de 3 en el grado x)))
- y=ln(√((1+sin5x)/(2-cos3^x)))
- y=ln(sqrt((1+sin5x)/(2-cos3x)))
- y=lnsqrt1+sin5x/2-cos3x
- y=lnsqrt1+sin5x/2-cos3^x
- y=ln(sqrt((1+sin5x) dividir por (2-cos3^x)))
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Expresiones semejantes
- y=ln(sqrt((1+sin5x)/(2+cos3^x)))
- y=ln(sqrt((1-sin5x)/(2-cos3^x)))
Derivada de y=ln(sqrt((1+sin5x)/(2-cos3^x)))
Solución
Ha introducido
[src]
/ ______________\ | / 1 + sin(5*x) | log| / ------------ | | / x | \\/ 2 - cos (3) /
$$\log{\left(\sqrt{\frac{\sin{\left(5 x \right)} + 1}{2 - \cos^{x}{\left(3 \right)}}} \right)}$$
log(sqrt((1 + sin(5*x))/(2 - cos(3)^x)))
Solución detallada
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Sustituimos .
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Derivado es .
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Luego se aplica una cadena de reglas. Multiplicamos por :
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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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Se aplica la regla de la derivada parcial:
y .
Para calcular :
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diferenciamos miembro por miembro:
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La derivada de una constante es igual a cero.
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Sustituimos .
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La derivada del seno es igual al coseno:
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Luego se aplica una cadena de reglas. Multiplicamos por :
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La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
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Según el principio, aplicamos: tenemos
Entonces, como resultado:
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Como resultado de la secuencia de reglas:
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Como resultado de:
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Para calcular :
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diferenciamos miembro por miembro:
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La derivada de una constante es igual a cero.
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La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.
Entonces, como resultado:
Como resultado de:
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Ahora aplicamos la regla de la derivada de una divesión:
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Como resultado de la secuencia de reglas:
Como resultado de la secuencia de reglas:
Simplificamos:
Respuesta:
Primera derivada
[src]
/ x \
/ x \ | 5*cos(5*x) cos (3)*(1 + sin(5*x))*(pi*I + log(-cos(3)))|
\2 - cos (3)/*|--------------- + --------------------------------------------|
| / x \ 2 |
|2*\2 - cos (3)/ / x \ |
\ 2*\2 - cos (3)/ /
------------------------------------------------------------------------------
1 + sin(5*x)
$$\frac{\left(2 - \cos^{x}{\left(3 \right)}\right) \left(\frac{5 \cos{\left(5 x \right)}}{2 \left(2 - \cos^{x}{\left(3 \right)}\right)} + \frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{2 \left(2 - \cos^{x}{\left(3 \right)}\right)^{2}}\right)}{\sin{\left(5 x \right)} + 1}$$
Segunda derivada
[src]
/ x \ / x \
| cos (3)*(1 + sin(5*x))*(pi*I + log(-cos(3)))| x | cos (3)*(1 + sin(5*x))*(pi*I + log(-cos(3)))|
5*|-5*cos(5*x) + --------------------------------------------|*cos(5*x) cos (3)*|-5*cos(5*x) + --------------------------------------------|*(pi*I + log(-cos(3)))
| x | 2 2*x x 2 x | x |
25*sin(5*x) \ -2 + cos (3) / (pi*I + log(-cos(3))) *cos (3)*(1 + sin(5*x)) 5*cos (3)*(pi*I + log(-cos(3)))*cos(5*x) (pi*I + log(-cos(3))) *cos (3)*(1 + sin(5*x)) \ -2 + cos (3) /
- ----------- + ----------------------------------------------------------------------- + ----------------------------------------------- - ---------------------------------------- - --------------------------------------------- - ------------------------------------------------------------------------------------------
2 2*(1 + sin(5*x)) 2 x / x \ / x \
/ x \ -2 + cos (3) 2*\-2 + cos (3)/ 2*\-2 + cos (3)/
\-2 + cos (3)/
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1 + sin(5*x)
$$\frac{- \frac{\left(\frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{\cos^{x}{\left(3 \right)} - 2} - 5 \cos{\left(5 x \right)}\right) \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \cos^{x}{\left(3 \right)}}{2 \left(\cos^{x}{\left(3 \right)} - 2\right)} + \frac{5 \left(\frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{\cos^{x}{\left(3 \right)} - 2} - 5 \cos{\left(5 x \right)}\right) \cos{\left(5 x \right)}}{2 \left(\sin{\left(5 x \right)} + 1\right)} - \frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{2 \left(\cos^{x}{\left(3 \right)} - 2\right)} + \frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \left(\sin{\left(5 x \right)} + 1\right) \cos^{2 x}{\left(3 \right)}}{\left(\cos^{x}{\left(3 \right)} - 2\right)^{2}} - \frac{25 \sin{\left(5 x \right)}}{2} - \frac{5 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \cos^{x}{\left(3 \right)} \cos{\left(5 x \right)}}{\cos^{x}{\left(3 \right)} - 2}}{\sin{\left(5 x \right)} + 1}$$
Tercera derivada
[src]
/ 2 x 2 2*x x \ / 2 x 2 2*x x \
/ x \ | (pi*I + log(-cos(3))) *cos (3)*(1 + sin(5*x)) 2*(pi*I + log(-cos(3))) *cos (3)*(1 + sin(5*x)) 10*cos (3)*(pi*I + log(-cos(3)))*cos(5*x)| / x \ x | (pi*I + log(-cos(3))) *cos (3)*(1 + sin(5*x)) 2*(pi*I + log(-cos(3))) *cos (3)*(1 + sin(5*x)) 10*cos (3)*(pi*I + log(-cos(3)))*cos(5*x)| / x \ / x \
2 | cos (3)*(1 + sin(5*x))*(pi*I + log(-cos(3)))| 5*|25*sin(5*x) + --------------------------------------------- - ------------------------------------------------- + -----------------------------------------|*cos(5*x) | cos (3)*(1 + sin(5*x))*(pi*I + log(-cos(3)))| cos (3)*(pi*I + log(-cos(3)))*|25*sin(5*x) + --------------------------------------------- - ------------------------------------------------- + -----------------------------------------| 2 x | cos (3)*(1 + sin(5*x))*(pi*I + log(-cos(3)))| x | cos (3)*(1 + sin(5*x))*(pi*I + log(-cos(3)))|
25*cos (5*x)*|-5*cos(5*x) + --------------------------------------------| | x 2 x | 25*|-5*cos(5*x) + --------------------------------------------|*sin(5*x) | x 2 x | (pi*I + log(-cos(3))) *cos (3)*|-5*cos(5*x) + --------------------------------------------| 5*cos (3)*|-5*cos(5*x) + --------------------------------------------|*(pi*I + log(-cos(3)))*cos(5*x)
| x | | -2 + cos (3) / x \ -2 + cos (3) | | x | | -2 + cos (3) / x \ -2 + cos (3) | 3 3*x 3 2*x 2 2*x 2 x | x | 3 x x | x |
125*cos(5*x) \ -2 + cos (3) / \ \-2 + cos (3)/ / \ -2 + cos (3) / \ \-2 + cos (3)/ / 3*(pi*I + log(-cos(3))) *cos (3)*(1 + sin(5*x)) 3*(pi*I + log(-cos(3))) *cos (3)*(1 + sin(5*x)) 15*(pi*I + log(-cos(3))) *cos (3)*cos(5*x) 15*(pi*I + log(-cos(3))) *cos (3)*cos(5*x) \ -2 + cos (3) / (pi*I + log(-cos(3))) *cos (3)*(1 + sin(5*x)) 75*cos (3)*(pi*I + log(-cos(3)))*sin(5*x) \ -2 + cos (3) /
- ------------ - ------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------- + ------------------------------------------------- + -------------------------------------------- - ------------------------------------------ - ------------------------------------------------------------------------------------------- - --------------------------------------------- + ----------------------------------------- + -----------------------------------------------------------------------------------------------------
2 2 1 + sin(5*x) 2*(1 + sin(5*x)) x 3 2 2 / x \ / x \ / x \ / x \ / x \
(1 + sin(5*x)) -2 + cos (3) / x \ / x \ / x \ 2*\-2 + cos (3)/ 2*\-2 + cos (3)/ 2*\-2 + cos (3)/ 2*\-2 + cos (3)/ (1 + sin(5*x))*\-2 + cos (3)/
\-2 + cos (3)/ \-2 + cos (3)/ \-2 + cos (3)/
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1 + sin(5*x)
$$\frac{- \frac{\left(\frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{\cos^{x}{\left(3 \right)} - 2} - 5 \cos{\left(5 x \right)}\right) \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \cos^{x}{\left(3 \right)}}{2 \left(\cos^{x}{\left(3 \right)} - 2\right)} - \frac{25 \left(\frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{\cos^{x}{\left(3 \right)} - 2} - 5 \cos{\left(5 x \right)}\right) \sin{\left(5 x \right)}}{2 \left(\sin{\left(5 x \right)} + 1\right)} + \frac{5 \left(\frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{\cos^{x}{\left(3 \right)} - 2} - 5 \cos{\left(5 x \right)}\right) \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \cos^{x}{\left(3 \right)} \cos{\left(5 x \right)}}{\left(\sin{\left(5 x \right)} + 1\right) \left(\cos^{x}{\left(3 \right)} - 2\right)} - \frac{25 \left(\frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{\cos^{x}{\left(3 \right)} - 2} - 5 \cos{\left(5 x \right)}\right) \cos^{2}{\left(5 x \right)}}{\left(\sin{\left(5 x \right)} + 1\right)^{2}} - \frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{3} \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{2 \left(\cos^{x}{\left(3 \right)} - 2\right)} + \frac{3 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{3} \left(\sin{\left(5 x \right)} + 1\right) \cos^{2 x}{\left(3 \right)}}{\left(\cos^{x}{\left(3 \right)} - 2\right)^{2}} - \frac{3 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{3} \left(\sin{\left(5 x \right)} + 1\right) \cos^{3 x}{\left(3 \right)}}{\left(\cos^{x}{\left(3 \right)} - 2\right)^{3}} - \frac{125 \cos{\left(5 x \right)}}{2} - \frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \left(\frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{\cos^{x}{\left(3 \right)} - 2} - \frac{2 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \left(\sin{\left(5 x \right)} + 1\right) \cos^{2 x}{\left(3 \right)}}{\left(\cos^{x}{\left(3 \right)} - 2\right)^{2}} + 25 \sin{\left(5 x \right)} + \frac{10 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \cos^{x}{\left(3 \right)} \cos{\left(5 x \right)}}{\cos^{x}{\left(3 \right)} - 2}\right) \cos^{x}{\left(3 \right)}}{\cos^{x}{\left(3 \right)} - 2} + \frac{75 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \sin{\left(5 x \right)} \cos^{x}{\left(3 \right)}}{2 \left(\cos^{x}{\left(3 \right)} - 2\right)} - \frac{15 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \cos^{x}{\left(3 \right)} \cos{\left(5 x \right)}}{2 \left(\cos^{x}{\left(3 \right)} - 2\right)} + \frac{15 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \cos^{2 x}{\left(3 \right)} \cos{\left(5 x \right)}}{\left(\cos^{x}{\left(3 \right)} - 2\right)^{2}} + \frac{5 \left(\frac{\left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \left(\sin{\left(5 x \right)} + 1\right) \cos^{x}{\left(3 \right)}}{\cos^{x}{\left(3 \right)} - 2} - \frac{2 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right)^{2} \left(\sin{\left(5 x \right)} + 1\right) \cos^{2 x}{\left(3 \right)}}{\left(\cos^{x}{\left(3 \right)} - 2\right)^{2}} + 25 \sin{\left(5 x \right)} + \frac{10 \left(\log{\left(- \cos{\left(3 \right)} \right)} + i \pi\right) \cos^{x}{\left(3 \right)} \cos{\left(5 x \right)}}{\cos^{x}{\left(3 \right)} - 2}\right) \cos{\left(5 x \right)}}{\sin{\left(5 x \right)} + 1}}{\sin{\left(5 x \right)} + 1}$$
Gráfico