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 x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Derivada de (t^(2)+1)÷(t^(1÷2)-1)
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Expresiones idénticas
- y=(sin√x)^cos5x
- y es igual a ( seno de √x) en el grado coseno de 5x
- y=(sin√x)cos5x
- y=sin√xcos5x
- y=sin√x^cos5x
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Expresiones con funciones
- Seno sin
- sin(x+2)
- sin(x)^sin(x)
- sin(x)/(1-x)
- sin(x^4)
- sin(x)/(1+tan(x))
Derivada de y=(sin√x)^cos5x
Solución
Ha introducido
[src]
cos(5*x)/ ___\ sin \\/ x /
$$\sin^{\cos{\left(5 x \right)}}{\left(\sqrt{x} \right)}$$
sin(sqrt(x))^cos(5*x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
/ / ___\ \
cos(5*x)/ ___\ | / / ___\\ cos\\/ x /*cos(5*x)|
sin \\/ x /*|- 5*log\sin\\/ x //*sin(5*x) + -------------------|
| ___ / ___\|
\ 2*\/ x *sin\\/ x //
$$\left(- 5 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(5 x \right)} + \frac{\cos{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{2 \sqrt{x} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\cos{\left(5 x \right)}}{\left(\sqrt{x} \right)}$$
Segunda derivada
[src]
/ 2 \
|/ / ___\ \ |
|| / / ___\\ cos\\/ x /*cos(5*x)| |
||10*log\sin\\/ x //*sin(5*x) - -------------------| |
|| ___ / ___\ | / ___\ 2/ ___\ / ___\ |
cos(5*x)/ ___\ |\ \/ x *sin\\/ x / / / / ___\\ cos(5*x) 5*cos\\/ x /*sin(5*x) cos \\/ x /*cos(5*x) cos\\/ x /*cos(5*x)|
sin \\/ x /*|---------------------------------------------------- - 25*cos(5*x)*log\sin\\/ x // - -------- - --------------------- - -------------------- - -------------------|
| 4 4*x ___ / ___\ 2/ ___\ 3/2 / ___\ |
\ \/ x *sin\\/ x / 4*x*sin \\/ x / 4*x *sin\\/ x / /
$$\left(\frac{\left(10 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(5 x \right)} - \frac{\cos{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}\right)^{2}}{4} - 25 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(5 x \right)} - \frac{\cos{\left(5 x \right)}}{4 x} - \frac{\cos^{2}{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{4 x \sin^{2}{\left(\sqrt{x} \right)}} - \frac{5 \sin{\left(5 x \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}} - \frac{\cos{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\cos{\left(5 x \right)}}{\left(\sqrt{x} \right)}$$
Tercera derivada
[src]
/ 3 \
| / / ___\ \ / / ___\ \ / 2/ ___\ / ___\ / ___\ \ |
| | / / ___\\ cos\\/ x /*cos(5*x)| | / / ___\\ cos\\/ x /*cos(5*x)| |cos(5*x) / / ___\\ cos \\/ x /*cos(5*x) cos\\/ x /*cos(5*x) 20*cos\\/ x /*sin(5*x)| |
| |10*log\sin\\/ x //*sin(5*x) - -------------------| 3*|10*log\sin\\/ x //*sin(5*x) - -------------------|*|-------- + 100*cos(5*x)*log\sin\\/ x // + -------------------- + ------------------- + ----------------------| |
| | ___ / ___\ | | ___ / ___\ | | x 2/ ___\ 3/2 / ___\ ___ / ___\ | / ___\ 3/ ___\ / ___\ 2/ ___\ / ___\ 2/ ___\ / ___\ |
cos(5*x)/ ___\ | \ \/ x *sin\\/ x / / / / ___\\ 3*cos(5*x) \ \/ x *sin\\/ x / / \ x*sin \\/ x / x *sin\\/ x / \/ x *sin\\/ x / / 15*sin(5*x) 75*cos\\/ x /*cos(5*x) cos \\/ x /*cos(5*x) cos\\/ x /*cos(5*x) 3*cos \\/ x /*cos(5*x) 3*cos\\/ x /*cos(5*x) 15*cos \\/ x /*sin(5*x) 15*cos\\/ x /*sin(5*x)|
sin \\/ x /*|- ---------------------------------------------------- + 125*log\sin\\/ x //*sin(5*x) + ---------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------- - ---------------------- + -------------------- + ------------------- + ---------------------- + --------------------- + ----------------------- + ----------------------|
| 8 2 8 4*x ___ / ___\ 3/2 3/ ___\ 3/2 / ___\ 2 2/ ___\ 5/2 / ___\ 2/ ___\ 3/2 / ___\ |
\ 8*x 2*\/ x *sin\\/ x / 4*x *sin \\/ x / 4*x *sin\\/ x / 8*x *sin \\/ x / 8*x *sin\\/ x / 4*x*sin \\/ x / 4*x *sin\\/ x / /
$$\left(- \frac{\left(10 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(5 x \right)} - \frac{\cos{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}\right)^{3}}{8} + \frac{3 \left(10 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(5 x \right)} - \frac{\cos{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}\right) \left(100 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(5 x \right)} + \frac{\cos{\left(5 x \right)}}{x} + \frac{\cos^{2}{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{20 \sin{\left(5 x \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}} + \frac{\cos{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}}\right)}{8} + 125 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin{\left(5 x \right)} + \frac{15 \sin{\left(5 x \right)}}{4 x} + \frac{15 \sin{\left(5 x \right)} \cos^{2}{\left(\sqrt{x} \right)}}{4 x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{3 \cos{\left(5 x \right)}}{8 x^{2}} + \frac{3 \cos^{2}{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{8 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} - \frac{75 \cos{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{2 \sqrt{x} \sin{\left(\sqrt{x} \right)}} + \frac{15 \sin{\left(5 x \right)} \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{\cos{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{\cos^{3}{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{4 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} + \frac{3 \cos{\left(\sqrt{x} \right)} \cos{\left(5 x \right)}}{8 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\cos{\left(5 x \right)}}{\left(\sqrt{x} \right)}$$
Gráfico