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 1/(x+1)^2
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Derivada de (x+3)/(x-2)
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Derivada de (x+4)^2*(x+1)+9
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Derivada de e^(2-x)
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Expresiones idénticas
- xlog2(sin((3x+ cuatro)/(x+ uno)))*exp(-x)
- x logaritmo de 2( seno de ((3x más 4) dividir por (x más 1))) multiplicar por exponente de ( menos x)
- x logaritmo de 2( seno de ((3x más cuatro) dividir por (x más uno))) multiplicar por exponente de ( menos x)
- xlog2(sin((3x+4)/(x+1)))exp(-x)
- xlog2sin3x+4/x+1exp-x
- xlog2(sin((3x+4) dividir por (x+1)))*exp(-x)
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Expresiones semejantes
- xlog2(sin((3x+4)/(x+1)))*exp(x)
- xlog2(sin((3x+4)/(x-1)))*exp(-x)
- xlog2(sin((3x-4)/(x+1)))*exp(-x)
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Expresiones con funciones
- Seno sin
- sin(sin(x))
- sin^2*2x
- sin(x/5)
- sin(8*x)
- sin²(x)
- Exponente exp
- exp(x^1/2)
- exp(2*x)
- exp(y)
Derivada de xlog2(sin((3x+4)/(x+1)))*exp(-x)
Solución
Ha introducido
[src]
/ /3*x + 4\\
log|sin|-------||
\ \ x + 1 // -x
x*-----------------*e
log(2)
$$x \frac{\log{\left(\sin{\left(\frac{3 x + 4}{x + 1} \right)} \right)}}{\log{\left(2 \right)}} e^{- x}$$
(x*(log(sin((3*x + 4)/(x + 1)))/log(2)))*exp(-x)
Primera derivada
[src]
/ / 3 3*x + 4 \ /3*x + 4\\ | / /3*x + 4\\ x*|----- - --------|*cos|-------|| -x / /3*x + 4\\ |log|sin|-------|| |x + 1 2| \ x + 1 /| x*e *log|sin|-------|| | \ \ x + 1 // \ (x + 1) / | -x \ \ x + 1 // |----------------- + ---------------------------------|*e - ----------------------- | log(2) /3*x + 4\ | log(2) | log(2)*sin|-------| | \ \ x + 1 / /
$$- \frac{x e^{- x} \log{\left(\sin{\left(\frac{3 x + 4}{x + 1} \right)} \right)}}{\log{\left(2 \right)}} + \left(\frac{x \left(\frac{3}{x + 1} - \frac{3 x + 4}{\left(x + 1\right)^{2}}\right) \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\log{\left(2 \right)} \sin{\left(\frac{3 x + 4}{x + 1} \right)}} + \frac{\log{\left(\sin{\left(\frac{3 x + 4}{x + 1} \right)} \right)}}{\log{\left(2 \right)}}\right) e^{- x}$$
Segunda derivada
[src]
/ / / /4 + 3*x\ 2/4 + 3*x\ / 4 + 3*x\\\ \
| | | 2*cos|-------| cos |-------|*|3 - -------||| |
| | | 4 + 3*x \ 1 + x / \ 1 + x / \ 1 + x /|| |
| | x*|3 - ------- + -------------- + ---------------------------|| |
| | /4 + 3*x\ | 1 + x /4 + 3*x\ 2/4 + 3*x\ || |
| | 2*cos|-------| | sin|-------| sin |-------| || |
| / 4 + 3*x\ | \ 1 + x / \ \ 1 + x / \ 1 + x / /| |
| |3 - -------|*|- -------------- + --------------------------------------------------------------| |
| \ 1 + x / | /4 + 3*x\ 1 + x | / 4 + 3*x\ /4 + 3*x\|
| | sin|-------| | 2*x*|3 - -------|*cos|-------||
| / /4 + 3*x\\ / /4 + 3*x\\ \ \ 1 + x / / \ 1 + x / \ 1 + x /| -x
|- 2*log|sin|-------|| + x*log|sin|-------|| - ------------------------------------------------------------------------------------------------- - ------------------------------|*e
| \ \ 1 + x // \ \ 1 + x // 1 + x /4 + 3*x\ |
| (1 + x)*sin|-------| |
\ \ 1 + x / /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(2)
$$\frac{\left(- \frac{2 x \left(3 - \frac{3 x + 4}{x + 1}\right) \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\left(x + 1\right) \sin{\left(\frac{3 x + 4}{x + 1} \right)}} + x \log{\left(\sin{\left(\frac{3 x + 4}{x + 1} \right)} \right)} - \frac{\left(3 - \frac{3 x + 4}{x + 1}\right) \left(\frac{x \left(\frac{\left(3 - \frac{3 x + 4}{x + 1}\right) \cos^{2}{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin^{2}{\left(\frac{3 x + 4}{x + 1} \right)}} + 3 + \frac{2 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}} - \frac{3 x + 4}{x + 1}\right)}{x + 1} - \frac{2 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}}\right)}{x + 1} - 2 \log{\left(\sin{\left(\frac{3 x + 4}{x + 1} \right)} \right)}\right) e^{- x}}{\log{\left(2 \right)}}$$
Tercera derivada
[src]
/ / / 2 2 \ \ \
| | | /4 + 3*x\ / 4 + 3*x\ 3/4 + 3*x\ / 4 + 3*x\ /4 + 3*x\ 2/4 + 3*x\ / 4 + 3*x\| | / / /4 + 3*x\ 2/4 + 3*x\ / 4 + 3*x\\\ |
| | | 3*cos|-------| |3 - -------| *cos |-------| |3 - -------| *cos|-------| 3*cos |-------|*|3 - -------|| | | | 2*cos|-------| cos |-------|*|3 - -------||| |
| | | 3*(4 + 3*x) \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x /| | | | 4 + 3*x \ 1 + x / \ 1 + x / \ 1 + x /|| |
| | 2*x*|9 - ----------- + -------------- + ---------------------------- + --------------------------- + -----------------------------| | | x*|3 - ------- + -------------- + ---------------------------|| |
| | /4 + 3*x\ | 1 + x /4 + 3*x\ 3/4 + 3*x\ /4 + 3*x\ 2/4 + 3*x\ | 2/4 + 3*x\ / 4 + 3*x\| | /4 + 3*x\ | 1 + x /4 + 3*x\ 2/4 + 3*x\ || |
| | 6*cos|-------| | sin|-------| sin |-------| sin|-------| sin |-------| | 3*cos |-------|*|3 - -------|| | 2*cos|-------| | sin|-------| sin |-------| || |
| / 4 + 3*x\ | 3*(4 + 3*x) \ 1 + x / \ \ 1 + x / \ 1 + x / \ 1 + x / \ 1 + x / / \ 1 + x / \ 1 + x /| / 4 + 3*x\ | \ 1 + x / \ \ 1 + x / \ 1 + x / /| |
| |3 - -------|*|9 - ----------- + -------------- - ----------------------------------------------------------------------------------------------------------------------------------- + -----------------------------| 3*|3 - -------|*|- -------------- + --------------------------------------------------------------| |
| \ 1 + x / | 1 + x /4 + 3*x\ 1 + x 2/4 + 3*x\ | \ 1 + x / | /4 + 3*x\ 1 + x | / 4 + 3*x\ /4 + 3*x\|
| | sin|-------| sin |-------| | | sin|-------| | 3*x*|3 - -------|*cos|-------||
| / /4 + 3*x\\ / /4 + 3*x\\ \ \ 1 + x / \ 1 + x / / \ \ 1 + x / / \ 1 + x / \ 1 + x /| -x
|3*log|sin|-------|| - x*log|sin|-------|| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------- + ------------------------------|*e
| \ \ 1 + x // \ \ 1 + x // 2 1 + x /4 + 3*x\ |
| (1 + x) (1 + x)*sin|-------| |
\ \ 1 + x / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(2)
$$\frac{\left(\frac{3 x \left(3 - \frac{3 x + 4}{x + 1}\right) \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\left(x + 1\right) \sin{\left(\frac{3 x + 4}{x + 1} \right)}} - x \log{\left(\sin{\left(\frac{3 x + 4}{x + 1} \right)} \right)} + \frac{3 \left(3 - \frac{3 x + 4}{x + 1}\right) \left(\frac{x \left(\frac{\left(3 - \frac{3 x + 4}{x + 1}\right) \cos^{2}{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin^{2}{\left(\frac{3 x + 4}{x + 1} \right)}} + 3 + \frac{2 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}} - \frac{3 x + 4}{x + 1}\right)}{x + 1} - \frac{2 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}}\right)}{x + 1} - \frac{\left(3 - \frac{3 x + 4}{x + 1}\right) \left(- \frac{2 x \left(\frac{\left(3 - \frac{3 x + 4}{x + 1}\right)^{2} \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}} + \frac{\left(3 - \frac{3 x + 4}{x + 1}\right)^{2} \cos^{3}{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin^{3}{\left(\frac{3 x + 4}{x + 1} \right)}} + \frac{3 \left(3 - \frac{3 x + 4}{x + 1}\right) \cos^{2}{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin^{2}{\left(\frac{3 x + 4}{x + 1} \right)}} + 9 + \frac{3 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}} - \frac{3 \left(3 x + 4\right)}{x + 1}\right)}{x + 1} + \frac{3 \left(3 - \frac{3 x + 4}{x + 1}\right) \cos^{2}{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin^{2}{\left(\frac{3 x + 4}{x + 1} \right)}} + 9 + \frac{6 \cos{\left(\frac{3 x + 4}{x + 1} \right)}}{\sin{\left(\frac{3 x + 4}{x + 1} \right)}} - \frac{3 \left(3 x + 4\right)}{x + 1}\right)}{\left(x + 1\right)^{2}} + 3 \log{\left(\sin{\left(\frac{3 x + 4}{x + 1} \right)} \right)}\right) e^{- x}}{\log{\left(2 \right)}}$$
Gráfico