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 2*sin(3*x)
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Derivada de 3*(2-x)^6
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Derivada de -(1/x)
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Derivada de y=-6/x
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Expresiones idénticas
- y=(arccosx)^ln^2x
- y es igual a (arc coseno de x) en el grado ln al cuadrado x
- y=(arccosx)ln2x
- y=arccosxln2x
- y=(arccosx)^ln²x
- y=(arccosx) en el grado ln en el grado 2x
- y=arccosx^ln^2x
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Expresiones con funciones
- ln
- ln(x+8)
- ln(x+1)²
- ln(1+x²)
- ln(x+10)^10
- ln(arcsinx)
Derivada de y=(arccosx)^ln^2x
Solución
Ha introducido
[src]
2
log (x)
(acos(x))
$$\operatorname{acos}^{\log{\left(x \right)}^{2}}{\left(x \right)}$$
acos(x)^(log(x)^2)
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 \
log (x) | log (x) 2*log(x)*log(acos(x))|
(acos(x)) *|- ------------------- + ---------------------|
| ________ x |
| / 2 |
\ \/ 1 - x *acos(x) /
$$\left(- \frac{\log{\left(x \right)}^{2}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + \frac{2 \log{\left(x \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x}\right) \operatorname{acos}^{\log{\left(x \right)}^{2}}{\left(x \right)}$$
Segunda derivada
[src]
2 / 2 2 2 \
log (x) |/ 2*log(acos(x)) log(x) \ 2 2*log(acos(x)) log (x) 2*log(x)*log(acos(x)) x*log (x) 4*log(x) |
(acos(x)) *||- -------------- + -------------------| *log (x) + -------------- + ------------------ - --------------------- - ------------------- - ---------------------|
|| x ________ | 2 / 2\ 2 2 3/2 ________ |
|| / 2 | x \-1 + x /*acos (x) x / 2\ / 2 |
\\ \/ 1 - x *acos(x)/ \1 - x / *acos(x) x*\/ 1 - x *acos(x)/
$$\left(- \frac{x \log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x}\right)^{2} \log{\left(x \right)}^{2} + \frac{\log{\left(x \right)}^{2}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{4 \log{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(x \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2}} + \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2}}\right) \operatorname{acos}^{\log{\left(x \right)}^{2}}{\left(x \right)}$$
Tercera derivada
[src]
2 / 3 2 2 / 2 2 \ 2 2 2 \
log (x) | / 2*log(acos(x)) log(x) \ 3 6*log(acos(x)) log (x) 6 6*log(x) 2*log (x) / 2*log(acos(x)) log(x) \ | 2*log(acos(x)) log (x) 2*log(x)*log(acos(x)) x*log (x) 4*log(x) | 4*log(x)*log(acos(x)) 3*x*log (x) 3*x *log (x) 6*log(x) 6*log(x) |
(acos(x)) *|- |- -------------- + -------------------| *log (x) - -------------- - ------------------- - ---------------------- - ------------------- - -------------------- + 3*|- -------------- + -------------------|*|- -------------- - ------------------ + --------------------- + ------------------- + ---------------------|*log(x) + --------------------- - ------------------- - ------------------- + -------------------- + ----------------------|
| | x ________ | 3 3/2 ________ 3/2 3/2 | x ________ | | 2 / 2\ 2 2 3/2 ________ | 3 2 5/2 / 2\ 2 ________ |
| | / 2 | x / 2\ 2 / 2 / 2\ / 2\ 3 | / 2 | | x \-1 + x /*acos (x) x / 2\ / 2 | x / 2\ 2 / 2\ x*\-1 + x /*acos (x) 2 / 2 |
\ \ \/ 1 - x *acos(x)/ \1 - x / *acos(x) x *\/ 1 - x *acos(x) \1 - x / *acos(x) \1 - x / *acos (x) \ \/ 1 - x *acos(x)/ \ \1 - x / *acos(x) x*\/ 1 - x *acos(x)/ \-1 + x / *acos (x) \1 - x / *acos(x) x *\/ 1 - x *acos(x)/
$$\left(- \frac{3 x^{2} \log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{acos}{\left(x \right)}} - \frac{3 x \log{\left(x \right)}^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(x \right)}} - \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x}\right)^{3} \log{\left(x \right)}^{3} + 3 \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x}\right) \left(\frac{x \log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{\log{\left(x \right)}^{2}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} + \frac{4 \log{\left(x \right)}}{x \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + \frac{2 \log{\left(x \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2}} - \frac{2 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{2}}\right) \log{\left(x \right)} - \frac{\log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \log{\left(x \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(x \right)}} - \frac{6 \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \frac{6 \log{\left(x \right)}}{x \left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} + \frac{6 \log{\left(x \right)}}{x^{2} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{6}{x^{2} \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + \frac{4 \log{\left(x \right)} \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{3}} - \frac{6 \log{\left(\operatorname{acos}{\left(x \right)} \right)}}{x^{3}}\right) \operatorname{acos}^{\log{\left(x \right)}^{2}}{\left(x \right)}$$
Gráfico