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^-(4/5)
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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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Expresiones idénticas
- y=(sin√x)^(ln(sin√x))
- y es igual a ( seno de √x) en el grado (ln( seno de √x))
- y=(sin√x)(ln(sin√x))
- y=sin√xlnsin√x
- y=sin√x^lnsin√x
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Expresiones con funciones
- Seno sin
- sin(x+2)
- sin(x)/2-cos(x)/2+10*e^(-x)
- sin(x)^(2)/2
- sin(x^3)^2
- sin(x)^-1
- ln
- ln(x/5)
- ln(e^(2*x)+1)
- ln(x^2+2)
- ln(1+x²)
- ln√x-2
- Seno sin
- sin(x+2)
- sin(x)/2-cos(x)/2+10*e^(-x)
- sin(x)^(2)/2
- sin(x^3)^2
- sin(x)^-1
Derivada de y=(sin√x)^(ln(sin√x))
Solución
Ha introducido
[src]
/ / ___\\
log\sin\\/ x //
/ / ___\\
\sin\\/ x //
$$\sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)}$$
sin(sqrt(x))^log(sin(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]
/ / ___\\
log\sin\\/ x //
/ / ___\\ / ___\ / / ___\\
\sin\\/ x // *cos\\/ x /*log\sin\\/ x //
------------------------------------------------------
___ / ___\
\/ x *sin\\/ x /
$$\frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}$$
Segunda derivada
[src]
/ / ___\\
log\sin\\/ x // / / / ___\\ 2/ ___\ 2/ ___\ 2/ / ___\\ 2/ ___\ / / ___\\ / ___\ / / ___\\\
/ / ___\\ | log\sin\\/ x // cos \\/ x / cos \\/ x /*log \sin\\/ x // cos \\/ x /*log\sin\\/ x // cos\\/ x /*log\sin\\/ x //|
\sin\\/ x // *|- --------------- + --------------- + ---------------------------- - --------------------------- - --------------------------|
| 2*x 2/ ___\ 2/ ___\ 2/ ___\ 3/2 / ___\ |
\ 2*x*sin \\/ x / x*sin \\/ x / 2*x*sin \\/ x / 2*x *sin\\/ x / /
$$\left(\frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{2}{\left(\sqrt{x} \right)}}{x \sin^{2}{\left(\sqrt{x} \right)}} - \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{2 x} - \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{2 x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{\cos^{2}{\left(\sqrt{x} \right)}}{2 x \sin^{2}{\left(\sqrt{x} \right)}} - \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)}$$
Tercera derivada
[src]
/ / ___\\
log\sin\\/ x // / / / ___\\ 2/ ___\ 3/ ___\ / ___\ 3/ ___\ 3/ / ___\\ / ___\ / / ___\\ 3/ ___\ / / ___\\ 2/ ___\ 2/ / ___\\ 3/ ___\ 2/ / ___\\ 2/ / ___\\ / ___\ 2/ ___\ / / ___\\ / ___\ / / ___\\\
/ / ___\\ |3*log\sin\\/ x // 3*cos \\/ x / 3*cos \\/ x / 3*cos\\/ x / cos \\/ x /*log \sin\\/ x // cos\\/ x /*log\sin\\/ x // 2*cos \\/ x /*log\sin\\/ x // 3*cos \\/ x /*log \sin\\/ x // 3*cos \\/ x /*log \sin\\/ x // 3*log \sin\\/ x //*cos\\/ x / 3*cos \\/ x /*log\sin\\/ x // 3*cos\\/ x /*log\sin\\/ x //|
\sin\\/ x // *|----------------- - ---------------- - ------------------ - ----------------- + ---------------------------- + -------------------------- + ----------------------------- - ------------------------------ - ------------------------------ - ----------------------------- + ----------------------------- + ----------------------------|
| 2 2 2/ ___\ 3/2 3/ ___\ 3/2 / ___\ 3/2 3/ ___\ 3/2 / ___\ 3/2 3/ ___\ 2 2/ ___\ 3/2 3/ ___\ 3/2 / ___\ 2 2/ ___\ 5/2 / ___\ |
\ 4*x 4*x *sin \\/ x / 4*x *sin \\/ x / 4*x *sin\\/ x / x *sin \\/ x / 2*x *sin\\/ x / x *sin \\/ x / 2*x *sin \\/ x / 2*x *sin \\/ x / 2*x *sin\\/ x / 4*x *sin \\/ x / 4*x *sin\\/ x / /
$$\left(- \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{2}{\left(\sqrt{x} \right)}}{2 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{4 x^{2}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{4 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} - \frac{3 \cos^{2}{\left(\sqrt{x} \right)}}{4 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} + \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{3} \cos^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} - \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} - \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{3}{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} + \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} - \frac{3 \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} - \frac{3 \cos^{3}{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)}$$
3-я производная
[src]
/ / ___\\
log\sin\\/ x // / / / ___\\ 2/ ___\ 3/ ___\ / ___\ 3/ ___\ 3/ / ___\\ / ___\ / / ___\\ 3/ ___\ / / ___\\ 2/ ___\ 2/ / ___\\ 3/ ___\ 2/ / ___\\ 2/ / ___\\ / ___\ 2/ ___\ / / ___\\ / ___\ / / ___\\\
/ / ___\\ |3*log\sin\\/ x // 3*cos \\/ x / 3*cos \\/ x / 3*cos\\/ x / cos \\/ x /*log \sin\\/ x // cos\\/ x /*log\sin\\/ x // 2*cos \\/ x /*log\sin\\/ x // 3*cos \\/ x /*log \sin\\/ x // 3*cos \\/ x /*log \sin\\/ x // 3*log \sin\\/ x //*cos\\/ x / 3*cos \\/ x /*log\sin\\/ x // 3*cos\\/ x /*log\sin\\/ x //|
\sin\\/ x // *|----------------- - ---------------- - ------------------ - ----------------- + ---------------------------- + -------------------------- + ----------------------------- - ------------------------------ - ------------------------------ - ----------------------------- + ----------------------------- + ----------------------------|
| 2 2 2/ ___\ 3/2 3/ ___\ 3/2 / ___\ 3/2 3/ ___\ 3/2 / ___\ 3/2 3/ ___\ 2 2/ ___\ 3/2 3/ ___\ 3/2 / ___\ 2 2/ ___\ 5/2 / ___\ |
\ 4*x 4*x *sin \\/ x / 4*x *sin \\/ x / 4*x *sin\\/ x / x *sin \\/ x / 2*x *sin\\/ x / x *sin \\/ x / 2*x *sin \\/ x / 2*x *sin \\/ x / 2*x *sin\\/ x / 4*x *sin \\/ x / 4*x *sin\\/ x / /
$$\left(- \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{2}{\left(\sqrt{x} \right)}}{2 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{4 x^{2}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{4 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} - \frac{3 \cos^{2}{\left(\sqrt{x} \right)}}{4 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} + \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{3} \cos^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} - \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} - \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{3}{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} + \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} - \frac{3 \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} - \frac{3 \cos^{3}{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)}$$
Gráfico