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 t
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Derivada de √x^3
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Derivada de e^1/x
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Derivada de e^1
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Expresiones idénticas
- y=cos5x^sin3√x
- y es igual a coseno de 5x en el grado seno de 3√x
- y=cos5xsin3√x
Derivada de y=cos5x^sin3√x
Solución
Ha introducido
[src]
/ ___\
sin\3*\/ x /
(cos(5*x))
$$\cos^{\sin{\left(3 \sqrt{x} \right)}}{\left(5 x \right)}$$
cos(5*x)^sin(3*sqrt(x))
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ ___\ / / ___\ / ___\ \
sin\3*\/ x / | 5*sin\3*\/ x /*sin(5*x) 3*cos\3*\/ x /*log(cos(5*x))|
(cos(5*x)) *|- ----------------------- + ----------------------------|
| cos(5*x) ___ |
\ 2*\/ x /
$$\left(- \frac{5 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} + \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{2 \sqrt{x}}\right) \cos^{\sin{\left(3 \sqrt{x} \right)}}{\left(5 x \right)}$$
Segunda derivada
[src]
/ 2 \
| / / ___\ / ___\ \ |
| | 3*cos\3*\/ x /*log(cos(5*x)) 10*sin\3*\/ x /*sin(5*x)| |
| |- ---------------------------- + ------------------------| |
/ ___\ | | ___ cos(5*x) | 2 / ___\ / ___\ / ___\ / ___\ |
sin\3*\/ x / | / ___\ \ \/ x / 25*sin (5*x)*sin\3*\/ x / 9*log(cos(5*x))*sin\3*\/ x / 3*cos\3*\/ x /*log(cos(5*x)) 15*cos\3*\/ x /*sin(5*x)|
(cos(5*x)) *|- 25*sin\3*\/ x / + ------------------------------------------------------------ - ------------------------- - ---------------------------- - ---------------------------- - ------------------------|
| 4 2 4*x 3/2 ___ |
\ cos (5*x) 4*x \/ x *cos(5*x) /
$$\left(\frac{\left(\frac{10 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x}}\right)^{2}}{4} - \frac{25 \sin{\left(3 \sqrt{x} \right)} \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} - 25 \sin{\left(3 \sqrt{x} \right)} - \frac{9 \log{\left(\cos{\left(5 x \right)} \right)} \sin{\left(3 \sqrt{x} \right)}}{4 x} - \frac{15 \sin{\left(5 x \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x} \cos{\left(5 x \right)}} - \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{4 x^{\frac{3}{2}}}\right) \cos^{\sin{\left(3 \sqrt{x} \right)}}{\left(5 x \right)}$$
Tercera derivada
[src]
/ 3 \
| / / ___\ / ___\ \ / / ___\ / ___\ \ / / ___\ / ___\ 2 / ___\ / ___\ \ |
| | 3*cos\3*\/ x /*log(cos(5*x)) 10*sin\3*\/ x /*sin(5*x)| | 3*cos\3*\/ x /*log(cos(5*x)) 10*sin\3*\/ x /*sin(5*x)| | / ___\ 3*cos\3*\/ x /*log(cos(5*x)) 9*log(cos(5*x))*sin\3*\/ x / 100*sin (5*x)*sin\3*\/ x / 60*cos\3*\/ x /*sin(5*x)| |
| |- ---------------------------- + ------------------------| 3*|- ---------------------------- + ------------------------|*|100*sin\3*\/ x / + ---------------------------- + ---------------------------- + -------------------------- + ------------------------| |
/ ___\ | | ___ cos(5*x) | / ___\ | ___ cos(5*x) | | 3/2 x 2 ___ | / ___\ 3 / ___\ / ___\ / ___\ / ___\ 2 / ___\ / ___\ / ___\ |
sin\3*\/ x / | \ \/ x / 225*cos\3*\/ x / \ \/ x / \ x cos (5*x) \/ x *cos(5*x) / 250*sin\3*\/ x /*sin(5*x) 250*sin (5*x)*sin\3*\/ x / 27*cos\3*\/ x /*log(cos(5*x)) 9*cos\3*\/ x /*log(cos(5*x)) 27*log(cos(5*x))*sin\3*\/ x / 225*sin (5*x)*cos\3*\/ x / 45*cos\3*\/ x /*sin(5*x) 135*sin\3*\/ x /*sin(5*x)|
(cos(5*x)) *|- ------------------------------------------------------------ - ---------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------- - -------------------------- - ----------------------------- + ---------------------------- + ----------------------------- - -------------------------- + ------------------------ + -------------------------|
| 8 ___ 8 cos(5*x) 3 3/2 5/2 2 ___ 2 3/2 4*x*cos(5*x) |
\ 2*\/ x cos (5*x) 8*x 8*x 8*x 2*\/ x *cos (5*x) 4*x *cos(5*x) /
$$\left(- \frac{\left(\frac{10 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x}}\right)^{3}}{8} + \frac{3 \left(\frac{10 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} - \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x}}\right) \left(\frac{100 \sin{\left(3 \sqrt{x} \right)} \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 100 \sin{\left(3 \sqrt{x} \right)} + \frac{9 \log{\left(\cos{\left(5 x \right)} \right)} \sin{\left(3 \sqrt{x} \right)}}{x} + \frac{60 \sin{\left(5 x \right)} \cos{\left(3 \sqrt{x} \right)}}{\sqrt{x} \cos{\left(5 x \right)}} + \frac{3 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{x^{\frac{3}{2}}}\right)}{8} - \frac{250 \sin{\left(3 \sqrt{x} \right)} \sin^{3}{\left(5 x \right)}}{\cos^{3}{\left(5 x \right)}} - \frac{250 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} + \frac{135 \sin{\left(3 \sqrt{x} \right)} \sin{\left(5 x \right)}}{4 x \cos{\left(5 x \right)}} + \frac{27 \log{\left(\cos{\left(5 x \right)} \right)} \sin{\left(3 \sqrt{x} \right)}}{8 x^{2}} - \frac{225 \sin^{2}{\left(5 x \right)} \cos{\left(3 \sqrt{x} \right)}}{2 \sqrt{x} \cos^{2}{\left(5 x \right)}} - \frac{225 \cos{\left(3 \sqrt{x} \right)}}{2 \sqrt{x}} - \frac{27 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{8 x^{\frac{3}{2}}} + \frac{45 \sin{\left(5 x \right)} \cos{\left(3 \sqrt{x} \right)}}{4 x^{\frac{3}{2}} \cos{\left(5 x \right)}} + \frac{9 \log{\left(\cos{\left(5 x \right)} \right)} \cos{\left(3 \sqrt{x} \right)}}{8 x^{\frac{5}{2}}}\right) \cos^{\sin{\left(3 \sqrt{x} \right)}}{\left(5 x \right)}$$
Gráfico