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- 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*sin(x)
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Derivada de x*e^(1/x)
- Derivada de x!
-
Derivada de e^y
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Expresiones idénticas
- y=ln(cuatro ^x+ cinco ^x^ dos)^(uno /x)
- y es igual a ln(4 en el grado x más 5 en el grado x al cuadrado ) en el grado (1 dividir por x)
- y es igual a ln(cuatro en el grado x más cinco en el grado x en el grado dos) en el grado (uno dividir por x)
- y=ln(4x+5x2)(1/x)
- y=ln4x+5x21/x
- y=ln(4^x+5^x²)^(1/x)
- y=ln(4 en el grado x+5 en el grado x en el grado 2) en el grado (1/x)
- y=ln4^x+5^x^2^1/x
- y=ln(4^x+5^x^2)^(1 dividir por x)
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Expresiones semejantes
- y=ln(4^x-5^x^2)^(1/x)
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Expresiones con funciones
- ln
- ln(x+√(x²+1))
- ln(x-4)
- ln(x²+2x)
- ln(x^2+2x)
- ln((x+1)÷(x-1))
Derivada de y=ln(4^x+5^x^2)^(1/x)
Solución
Ha introducido
[src]
_________________ / / / 2\\ x / | x \x /| \/ log\4 + 5 /
$$\log{\left(4^{x} + 5^{x^{2}} \right)}^{\frac{1}{x}}$$
log(4^x + 5^(x^2))^(1/x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
_________________ / / / / 2\\\ / 2\ \
/ / / 2\\ | | | x \x /|| x \x / |
x / | x \x /| | log\log\4 + 5 // 4 *log(4) + 2*x*5 *log(5) |
\/ log\4 + 5 / *|- -------------------- + ------------------------------|
| 2 / / 2\\ / / 2\\|
| x | x \x /| | x \x /||
\ x*\4 + 5 /*log\4 + 5 //
$$\left(\frac{4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}}{x \left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{\log{\left(\log{\left(4^{x} + 5^{x^{2}} \right)} \right)}}{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}^{\frac{1}{x}}$$
Segunda derivada
[src]
/ 2 \
|/ / / / 2\\\ / 2\ \ |
|| | | x \x /|| x \x / | |
|| log\log\4 + 5 // 4 *log(4) + 2*x*5 *log(5)| |
||- -------------------- + ----------------------------| 2 2 |
_________________ || x / / 2\\ / / 2\\| / / / 2\\\ / 2\ / 2\ / / 2\ \ / / 2\ \ / / 2\ \|
/ / / 2\\ || | x \x /| | x \x /|| | | x \x /|| x 2 \x / \x / 2 2 | x \x / | | x \x / | | x \x / ||
x / | x \x /| |\ \4 + 5 /*log\4 + 5 // 2*log\log\4 + 5 // 4 *log (4) + 2*5 *log(5) + 4*5 *x *log (5) \4 *log(4) + 2*x*5 *log(5)/ \4 *log(4) + 2*x*5 *log(5)/ 2*\4 *log(4) + 2*x*5 *log(5)/|
\/ log\4 + 5 / *|-------------------------------------------------------- + ---------------------- + ------------------------------------------------ - ------------------------------- - ------------------------------- - --------------------------------|
| x 2 / / 2\\ / / 2\\ 2 2 / / 2\\ / / 2\\ |
| x | x \x /| | x \x /| / / 2\\ / / 2\\ / / 2\\ / / 2\\ | x \x /| | x \x /| |
| \4 + 5 /*log\4 + 5 / | x \x /| | x \x /| | x \x /| 2| x \x /| x*\4 + 5 /*log\4 + 5 / |
\ \4 + 5 / *log\4 + 5 / \4 + 5 / *log \4 + 5 / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{\left(\frac{4^{x} \log{\left(4 \right)}^{2} + 4 \cdot 5^{x^{2}} x^{2} \log{\left(5 \right)}^{2} + 2 \cdot 5^{x^{2}} \log{\left(5 \right)}}{\left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{\left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)^{2}}{\left(4^{x} + 5^{x^{2}}\right)^{2} \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{\left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)^{2}}{\left(4^{x} + 5^{x^{2}}\right)^{2} \log{\left(4^{x} + 5^{x^{2}} \right)}^{2}} + \frac{\left(\frac{4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}}{\left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{\log{\left(\log{\left(4^{x} + 5^{x^{2}} \right)} \right)}}{x}\right)^{2}}{x} - \frac{2 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)}{x \left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} + \frac{2 \log{\left(\log{\left(4^{x} + 5^{x^{2}} \right)} \right)}}{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}^{\frac{1}{x}}}{x}$$
Tercera derivada
[src]
/ / 2 2 \ \
| 3 / / / / 2\\\ / 2\ \ | / / / 2\\\ / / 2\ \ / / 2\ \ / 2\ / 2\ / / 2\ \| |
|/ / / / 2\\\ / 2\ \ | | | x \x /|| x \x / | | | | x \x /|| | x \x / | | x \x / | x 2 \x / \x / 2 2 | x \x / || |
|| | | x \x /|| x \x / | | log\log\4 + 5 // 4 *log(4) + 2*x*5 *log(5)| | 2*log\log\4 + 5 // \4 *log(4) + 2*x*5 *log(5)/ \4 *log(4) + 2*x*5 *log(5)/ 4 *log (4) + 2*5 *log(5) + 4*5 *x *log (5) 2*\4 *log(4) + 2*x*5 *log(5)/| |
|| log\log\4 + 5 // 4 *log(4) + 2*x*5 *log(5)| 3*|- -------------------- + ----------------------------|*|- ---------------------- + ------------------------------- + ------------------------------- - ------------------------------------------------ + --------------------------------| |
||- -------------------- + ----------------------------| | x / / 2\\ / / 2\\| | 2 2 2 / / 2\\ / / 2\\ / / 2\\ / / 2\\ | 3 3 3 2 2 |
_________________ || x / / 2\\ / / 2\\| / / / 2\\\ / 2\ / 2\ | | x \x /| | x \x /|| | x / / 2\\ / / 2\\ / / 2\\ / / 2\\ | x \x /| | x \x /| | x \x /| | x \x /| | / / 2\ \ / / 2\ \ / / 2\ \ / / 2\ / 2\ \ / / 2\ \ / / 2\ / 2\ \ / / 2\ \ / / 2\ / 2\ \ / / 2\ \ / / 2\ \ / / 2\ \|
/ / / 2\\ || | x \x /| | x \x /|| | | x \x /|| x 3 \x / 3 3 \x / 2 \ \4 + 5 /*log\4 + 5 // | | x \x /| | x \x /| | x \x /| 2| x \x /| \4 + 5 /*log\4 + 5 / x*\4 + 5 /*log\4 + 5 / | | x \x / | | x \x / | | x \x / | | x 2 \x / \x / 2 2 | | x \x / | | x 2 \x / \x / 2 2 | | x \x / | | x 2 \x / \x / 2 2 | | x \x / | | x \x / | | x \x / ||
x / | x \x /| |\ \4 + 5 /*log\4 + 5 // 6*log\log\4 + 5 // 4 *log (4) + 8*5 *x *log (5) + 12*x*5 *log (5) \ \4 + 5 / *log\4 + 5 / \4 + 5 / *log \4 + 5 / / 2*\4 *log(4) + 2*x*5 *log(5)/ 2*\4 *log(4) + 2*x*5 *log(5)/ 3*\4 *log(4) + 2*x*5 *log(5)/ 3*\4 *log (4) + 2*5 *log(5) + 4*5 *x *log (5)/ 3*\4 *log(4) + 2*x*5 *log(5)/*\4 *log (4) + 2*5 *log(5) + 4*5 *x *log (5)/ 3*\4 *log(4) + 2*x*5 *log(5)/*\4 *log (4) + 2*5 *log(5) + 4*5 *x *log (5)/ 3*\4 *log(4) + 2*x*5 *log(5)/ 3*\4 *log(4) + 2*x*5 *log(5)/ 6*\4 *log(4) + 2*x*5 *log(5)/|
\/ log\4 + 5 / *|-------------------------------------------------------- - ---------------------- + ---------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------- + --------------------------------- + --------------------------------- - ---------------------------------------------------- - ----------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------- + --------------------------------- + --------------------------------- + --------------------------------|
| 2 3 / / 2\\ / / 2\\ x 3 3 3 / / 2\\ / / 2\\ 2 2 2 2 / / 2\\ / / 2\\ |
| x x | x \x /| | x \x /| / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ | x \x /| | x \x /| / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ / / 2\\ 2 | x \x /| | x \x /| |
| \4 + 5 /*log\4 + 5 / | x \x /| | x \x /| | x \x /| 3| x \x /| | x \x /| 2| x \x /| x*\4 + 5 /*log\4 + 5 / | x \x /| | x \x /| | x \x /| 2| x \x /| | x \x /| | x \x /| | x \x /| 2| x \x /| x *\4 + 5 /*log\4 + 5 / |
\ \4 + 5 / *log\4 + 5 / \4 + 5 / *log \4 + 5 / \4 + 5 / *log \4 + 5 / \4 + 5 / *log\4 + 5 / \4 + 5 / *log \4 + 5 / x*\4 + 5 / *log\4 + 5 / x*\4 + 5 / *log \4 + 5 / /
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x
$$\frac{\left(\frac{4^{x} \log{\left(4 \right)}^{3} + 8 \cdot 5^{x^{2}} x^{3} \log{\left(5 \right)}^{3} + 12 \cdot 5^{x^{2}} x \log{\left(5 \right)}^{2}}{\left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{3 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right) \left(4^{x} \log{\left(4 \right)}^{2} + 4 \cdot 5^{x^{2}} x^{2} \log{\left(5 \right)}^{2} + 2 \cdot 5^{x^{2}} \log{\left(5 \right)}\right)}{\left(4^{x} + 5^{x^{2}}\right)^{2} \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{3 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right) \left(4^{x} \log{\left(4 \right)}^{2} + 4 \cdot 5^{x^{2}} x^{2} \log{\left(5 \right)}^{2} + 2 \cdot 5^{x^{2}} \log{\left(5 \right)}\right)}{\left(4^{x} + 5^{x^{2}}\right)^{2} \log{\left(4^{x} + 5^{x^{2}} \right)}^{2}} + \frac{2 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)^{3}}{\left(4^{x} + 5^{x^{2}}\right)^{3} \log{\left(4^{x} + 5^{x^{2}} \right)}} + \frac{3 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)^{3}}{\left(4^{x} + 5^{x^{2}}\right)^{3} \log{\left(4^{x} + 5^{x^{2}} \right)}^{2}} + \frac{2 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)^{3}}{\left(4^{x} + 5^{x^{2}}\right)^{3} \log{\left(4^{x} + 5^{x^{2}} \right)}^{3}} - \frac{3 \left(\frac{4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}}{\left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{\log{\left(\log{\left(4^{x} + 5^{x^{2}} \right)} \right)}}{x}\right) \left(- \frac{4^{x} \log{\left(4 \right)}^{2} + 4 \cdot 5^{x^{2}} x^{2} \log{\left(5 \right)}^{2} + 2 \cdot 5^{x^{2}} \log{\left(5 \right)}}{\left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} + \frac{\left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)^{2}}{\left(4^{x} + 5^{x^{2}}\right)^{2} \log{\left(4^{x} + 5^{x^{2}} \right)}} + \frac{\left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)^{2}}{\left(4^{x} + 5^{x^{2}}\right)^{2} \log{\left(4^{x} + 5^{x^{2}} \right)}^{2}} + \frac{2 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)}{x \left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{2 \log{\left(\log{\left(4^{x} + 5^{x^{2}} \right)} \right)}}{x^{2}}\right)}{x} - \frac{3 \left(4^{x} \log{\left(4 \right)}^{2} + 4 \cdot 5^{x^{2}} x^{2} \log{\left(5 \right)}^{2} + 2 \cdot 5^{x^{2}} \log{\left(5 \right)}\right)}{x \left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} + \frac{3 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)^{2}}{x \left(4^{x} + 5^{x^{2}}\right)^{2} \log{\left(4^{x} + 5^{x^{2}} \right)}} + \frac{3 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)^{2}}{x \left(4^{x} + 5^{x^{2}}\right)^{2} \log{\left(4^{x} + 5^{x^{2}} \right)}^{2}} + \frac{\left(\frac{4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}}{\left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{\log{\left(\log{\left(4^{x} + 5^{x^{2}} \right)} \right)}}{x}\right)^{3}}{x^{2}} + \frac{6 \left(4^{x} \log{\left(4 \right)} + 2 \cdot 5^{x^{2}} x \log{\left(5 \right)}\right)}{x^{2} \left(4^{x} + 5^{x^{2}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}} - \frac{6 \log{\left(\log{\left(4^{x} + 5^{x^{2}} \right)} \right)}}{x^{3}}\right) \log{\left(4^{x} + 5^{x^{2}} \right)}^{\frac{1}{x}}}{x}$$
Gráfico