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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 √2x
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Derivada de 25/x
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Derivada de x*arcsinx
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Derivada de 2^(5*x)
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Expresiones idénticas
- y=(cuatro /x+√4x)^cos(4x)
- y es igual a (4 dividir por x más √4x) en el grado coseno de (4x)
- y es igual a (cuatro dividir por x más √4x) en el grado coseno de (4x)
- y=(4/x+√4x)cos(4x)
- y=4/x+√4xcos4x
- y=4/x+√4x^cos4x
- y=(4 dividir por x+√4x)^cos(4x)
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Expresiones semejantes
- y=(4/x-√4x)^cos(4x)
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Expresiones con funciones
- Coseno cos
- cos(-3x)
- cos(2)
- cos^-1x
- cos(ax)+sin(ax)
- cos(log(x))+x^2*tan(x)
Derivada de y=(4/x+√4x)^cos(4x)
Solución
Ha introducido
[src]
cos(4*x) /4 _____\ |- + \/ 4*x | \x /
$$\left(\sqrt{4 x} + \frac{4}{x}\right)^{\cos{\left(4 x \right)}}$$
(4/x + sqrt(4*x))^cos(4*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ / ___\ \
| | 4 2*\/ x | |
| |- -- + -------|*cos(4*x)|
cos(4*x) | | 2 2*x | |
/4 _____\ | /4 _____\ \ x / |
|- + \/ 4*x | *|- 4*log|- + \/ 4*x |*sin(4*x) + -------------------------|
\x / | \x / 4 _____ |
| - + \/ 4*x |
\ x /
$$\left(\sqrt{4 x} + \frac{4}{x}\right)^{\cos{\left(4 x \right)}} \left(- 4 \log{\left(\sqrt{4 x} + \frac{4}{x} \right)} \sin{\left(4 x \right)} + \frac{\left(\frac{2 \sqrt{x}}{2 x} - \frac{4}{x^{2}}\right) \cos{\left(4 x \right)}}{\sqrt{4 x} + \frac{4}{x}}\right)$$
Segunda derivada
[src]
/ 2 \
|/ / 1 4 \ \ |
|| |----- - --|*cos(4*x)| |
|| | ___ 2| | |
|| / / ___ 2\\ \\/ x x / | 2 |
||8*log|2*|\/ x + -||*sin(4*x) - ---------------------| / 1 4 \ / 1 4 \ / 1 16\ |
|| \ \ x// ___ 2 | 4*|----- - --|*sin(4*x) |----- - --| *cos(4*x) |- ---- + --|*cos(4*x)|
cos(4*x) || \/ x + - | | ___ 2| | ___ 2| | 3/2 3| |
/ / ___ 2\\ |\ x / / / ___ 2\\ \\/ x x / \\/ x x / \ x x / |
|2*|\/ x + -|| *|-------------------------------------------------------- - 16*cos(4*x)*log|2*|\/ x + -|| - ----------------------- - ---------------------- + ----------------------|
\ \ x// | 4 \ \ x// ___ 2 2 / ___ 2\ |
| \/ x + - / ___ 2\ 4*|\/ x + -| |
| x 4*|\/ x + -| \ x/ |
\ \ x/ /
$$\left(2 \left(\sqrt{x} + \frac{2}{x}\right)\right)^{\cos{\left(4 x \right)}} \left(\frac{\left(\frac{16}{x^{3}} - \frac{1}{x^{\frac{3}{2}}}\right) \cos{\left(4 x \right)}}{4 \left(\sqrt{x} + \frac{2}{x}\right)} - \frac{\left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right)^{2} \cos{\left(4 x \right)}}{4 \left(\sqrt{x} + \frac{2}{x}\right)^{2}} - \frac{4 \left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right) \sin{\left(4 x \right)}}{\sqrt{x} + \frac{2}{x}} + \frac{\left(- \frac{\left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right) \cos{\left(4 x \right)}}{\sqrt{x} + \frac{2}{x}} + 8 \log{\left(2 \left(\sqrt{x} + \frac{2}{x}\right) \right)} \sin{\left(4 x \right)}\right)^{2}}{4} - 16 \log{\left(2 \left(\sqrt{x} + \frac{2}{x}\right) \right)} \cos{\left(4 x \right)}\right)$$
Tercera derivada
[src]
/ / 2 \ \
| 3 / / 1 4 \ \ | / 1 4 \ / 1 16\ / 1 4 \ | |
| / / 1 4 \ \ | |----- - --|*cos(4*x)| | |----- - --| *cos(4*x) |- ---- + --|*cos(4*x) 16*|----- - --|*sin(4*x)| |
| | |----- - --|*cos(4*x)| | | ___ 2| | | | ___ 2| | 3/2 3| | ___ 2| | |
| | | ___ 2| | | / / ___ 2\\ \\/ x x / | | / / ___ 2\\ \\/ x x / \ x x / \\/ x x / | |
| | / / ___ 2\\ \\/ x x / | 3*|8*log|2*|\/ x + -||*sin(4*x) - ---------------------|*|64*cos(4*x)*log|2*|\/ x + -|| + ---------------------- - ---------------------- + ------------------------| 2 3 |
| |8*log|2*|\/ x + -||*sin(4*x) - ---------------------| | \ \ x// ___ 2 | | \ \ x// 2 ___ 2 ___ 2 | / 1 4 \ / 1 16\ / 1 4 \ / 1 32\ / 1 4 \ / 1 4 \ / 1 16\ |
| | \ \ x// ___ 2 | | \/ x + - | | / ___ 2\ \/ x + - \/ x + - | 24*|----- - --|*cos(4*x) 3*|- ---- + --|*sin(4*x) 3*|----- - --| *sin(4*x) 3*|- ---- + --|*cos(4*x) |----- - --| *cos(4*x) 3*|----- - --|*|- ---- + --|*cos(4*x)|
cos(4*x) | | \/ x + - | \ x / | |\/ x + -| x x | | ___ 2| | 3/2 3| | ___ 2| | 5/2 4| | ___ 2| | ___ 2| | 3/2 3| |
/ / ___ 2\\ | \ x / / / ___ 2\\ \ \ x/ / \\/ x x / \ x x / \\/ x x / \ x x / \\/ x x / \\/ x x / \ x x / |
|2*|\/ x + -|| *|- -------------------------------------------------------- + 64*log|2*|\/ x + -||*sin(4*x) + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------ - ------------------------ + ------------------------ - ------------------------ + ---------------------- - -------------------------------------|
\ \ x// | 8 \ \ x// 8 ___ 2 ___ 2 2 / ___ 2\ 3 2 |
| \/ x + - \/ x + - / ___ 2\ 8*|\/ x + -| / ___ 2\ / ___ 2\ |
| x x |\/ x + -| \ x/ 4*|\/ x + -| 8*|\/ x + -| |
\ \ x/ \ x/ \ x/ /
$$\left(2 \left(\sqrt{x} + \frac{2}{x}\right)\right)^{\cos{\left(4 x \right)}} \left(- \frac{3 \left(\frac{32}{x^{4}} - \frac{1}{x^{\frac{5}{2}}}\right) \cos{\left(4 x \right)}}{8 \left(\sqrt{x} + \frac{2}{x}\right)} - \frac{3 \left(\frac{16}{x^{3}} - \frac{1}{x^{\frac{3}{2}}}\right) \left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right) \cos{\left(4 x \right)}}{8 \left(\sqrt{x} + \frac{2}{x}\right)^{2}} - \frac{3 \left(\frac{16}{x^{3}} - \frac{1}{x^{\frac{3}{2}}}\right) \sin{\left(4 x \right)}}{\sqrt{x} + \frac{2}{x}} + \frac{\left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right)^{3} \cos{\left(4 x \right)}}{4 \left(\sqrt{x} + \frac{2}{x}\right)^{3}} + \frac{3 \left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right)^{2} \sin{\left(4 x \right)}}{\left(\sqrt{x} + \frac{2}{x}\right)^{2}} - \frac{24 \left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right) \cos{\left(4 x \right)}}{\sqrt{x} + \frac{2}{x}} - \frac{\left(- \frac{\left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right) \cos{\left(4 x \right)}}{\sqrt{x} + \frac{2}{x}} + 8 \log{\left(2 \left(\sqrt{x} + \frac{2}{x}\right) \right)} \sin{\left(4 x \right)}\right)^{3}}{8} + \frac{3 \left(- \frac{\left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right) \cos{\left(4 x \right)}}{\sqrt{x} + \frac{2}{x}} + 8 \log{\left(2 \left(\sqrt{x} + \frac{2}{x}\right) \right)} \sin{\left(4 x \right)}\right) \left(- \frac{\left(\frac{16}{x^{3}} - \frac{1}{x^{\frac{3}{2}}}\right) \cos{\left(4 x \right)}}{\sqrt{x} + \frac{2}{x}} + \frac{\left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right)^{2} \cos{\left(4 x \right)}}{\left(\sqrt{x} + \frac{2}{x}\right)^{2}} + \frac{16 \left(- \frac{4}{x^{2}} + \frac{1}{\sqrt{x}}\right) \sin{\left(4 x \right)}}{\sqrt{x} + \frac{2}{x}} + 64 \log{\left(2 \left(\sqrt{x} + \frac{2}{x}\right) \right)} \cos{\left(4 x \right)}\right)}{8} + 64 \log{\left(2 \left(\sqrt{x} + \frac{2}{x}\right) \right)} \sin{\left(4 x \right)}\right)$$
Gráfico