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^4/3-x
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Derivada de x^-4/5
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Derivada de x=1
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Derivada de x^2*2^x
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Expresiones idénticas
- y=(arccosx)^(√cosx)
- y es igual a (arc coseno de x) en el grado (√ coseno de x)
- y=(arccosx)(√cosx)
- y=arccosx√cosx
- y=arccosx^√cosx
Derivada de y=(arccosx)^(√cosx)
Solución
Ha introducido
[src]
________
\/ cos(x)
(acos(x))
$$\operatorname{acos}^{\sqrt{\cos{\left(x \right)}}}{\left(x \right)}$$
acos(x)^(sqrt(cos(x)))
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
Primera derivada
[src]
________ / ________ \
\/ cos(x) | \/ cos(x) log(acos(x))*sin(x)|
(acos(x)) *|- ------------------- - -------------------|
| ________ ________ |
| / 2 2*\/ cos(x) |
\ \/ 1 - x *acos(x) /
$$\left(- \frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)} \sin{\left(x \right)}}{2 \sqrt{\cos{\left(x \right)}}} - \frac{\sqrt{\cos{\left(x \right)}}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \operatorname{acos}^{\sqrt{\cos{\left(x \right)}}}{\left(x \right)}$$
Segunda derivada
[src]
/ 2 \
|/ ________ \ |
||log(acos(x))*sin(x) 2*\/ cos(x) | |
||------------------- + -------------------| |
|| ________ ________ | |
________ || \/ cos(x) / 2 | ________ ________ 2 ________ |
\/ cos(x) |\ \/ 1 - x *acos(x)/ \/ cos(x) *log(acos(x)) \/ cos(x) sin (x)*log(acos(x)) sin(x) x*\/ cos(x) |
(acos(x)) *|-------------------------------------------- - ----------------------- + ------------------ - -------------------- + ------------------------------ - -------------------|
| 4 2 / 2\ 2 3/2 ________ 3/2 |
| \-1 + x /*acos (x) 4*cos (x) / 2 ________ / 2\ |
\ \/ 1 - x *acos(x)*\/ cos(x) \1 - x / *acos(x)/
$$\left(- \frac{x \sqrt{\cos{\left(x \right)}}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \frac{\left(\frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)} \sin{\left(x \right)}}{\sqrt{\cos{\left(x \right)}}} + \frac{2 \sqrt{\cos{\left(x \right)}}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right)^{2}}{4} - \frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)} \sin^{2}{\left(x \right)}}{4 \cos^{\frac{3}{2}}{\left(x \right)}} - \frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)} \sqrt{\cos{\left(x \right)}}}{2} + \frac{\sqrt{\cos{\left(x \right)}}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{\sqrt{1 - x^{2}} \sqrt{\cos{\left(x \right)}} \operatorname{acos}{\left(x \right)}}\right) \operatorname{acos}^{\sqrt{\cos{\left(x \right)}}}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 \
| / ________ \ / ________ \ / 2 ________ ________ \ |
| |log(acos(x))*sin(x) 2*\/ cos(x) | |log(acos(x))*sin(x) 2*\/ cos(x) | | ________ sin (x)*log(acos(x)) 4*\/ cos(x) 4*sin(x) 4*x*\/ cos(x) | |
| |------------------- + -------------------| 3*|------------------- + -------------------|*|2*\/ cos(x) *log(acos(x)) + -------------------- - ------------------ - ------------------------------ + -------------------| |
| | ________ ________ | | ________ ________ | | 3/2 / 2\ 2 ________ 3/2 | |
________ | | \/ cos(x) / 2 | | \/ cos(x) / 2 | | cos (x) \-1 + x /*acos (x) / 2 ________ / 2\ | ________ ________ 3 ________ ________ 2 ________ 2 |
\/ cos(x) | \ \/ 1 - x *acos(x)/ \ \/ 1 - x *acos(x)/ \ \/ 1 - x *acos(x)*\/ cos(x) \1 - x / *acos(x)/ \/ cos(x) 2*\/ cos(x) 3*sin (x)*log(acos(x)) log(acos(x))*sin(x) 3*\/ cos(x) 3*x*\/ cos(x) 3*x *\/ cos(x) 3*sin(x) 3*sin (x) 3*x*sin(x) |
(acos(x)) *|- -------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------- - -------------------- - ---------------------- - ------------------- + --------------------- - ------------------- - ------------------- - ------------------------------- + ------------------------------- + --------------------------------|
| 8 8 3/2 3/2 5/2 ________ ________ 2 5/2 / 2\ 2 ________ ________ 3/2 |
| / 2\ / 2\ 3 8*cos (x) 4*\/ cos(x) / 2 / 2\ 2 / 2\ 2*\-1 + x /*acos (x)*\/ cos(x) / 2 3/2 / 2\ ________|
\ \1 - x / *acos(x) \1 - x / *acos (x) 2*\/ 1 - x *acos(x) \-1 + x / *acos (x) \1 - x / *acos(x) 4*\/ 1 - x *acos(x)*cos (x) 2*\1 - x / *acos(x)*\/ cos(x) /
$$\left(- \frac{3 x^{2} \sqrt{\cos{\left(x \right)}}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{acos}{\left(x \right)}} - \frac{3 x \sqrt{\cos{\left(x \right)}}}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(x \right)}} + \frac{3 x \sin{\left(x \right)}}{2 \left(1 - x^{2}\right)^{\frac{3}{2}} \sqrt{\cos{\left(x \right)}} \operatorname{acos}{\left(x \right)}} - \frac{\left(\frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)} \sin{\left(x \right)}}{\sqrt{\cos{\left(x \right)}}} + \frac{2 \sqrt{\cos{\left(x \right)}}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right)^{3}}{8} + \frac{3 \left(\frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)} \sin{\left(x \right)}}{\sqrt{\cos{\left(x \right)}}} + \frac{2 \sqrt{\cos{\left(x \right)}}}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}}\right) \left(\frac{4 x \sqrt{\cos{\left(x \right)}}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)} \sin^{2}{\left(x \right)}}{\cos^{\frac{3}{2}}{\left(x \right)}} + 2 \log{\left(\operatorname{acos}{\left(x \right)} \right)} \sqrt{\cos{\left(x \right)}} - \frac{4 \sqrt{\cos{\left(x \right)}}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}} - \frac{4 \sin{\left(x \right)}}{\sqrt{1 - x^{2}} \sqrt{\cos{\left(x \right)}} \operatorname{acos}{\left(x \right)}}\right)}{8} - \frac{3 \log{\left(\operatorname{acos}{\left(x \right)} \right)} \sin^{3}{\left(x \right)}}{8 \cos^{\frac{5}{2}}{\left(x \right)}} - \frac{\log{\left(\operatorname{acos}{\left(x \right)} \right)} \sin{\left(x \right)}}{4 \sqrt{\cos{\left(x \right)}}} - \frac{3 \sin{\left(x \right)}}{2 \left(x^{2} - 1\right) \sqrt{\cos{\left(x \right)}} \operatorname{acos}^{2}{\left(x \right)}} + \frac{3 \sin^{2}{\left(x \right)}}{4 \sqrt{1 - x^{2}} \cos^{\frac{3}{2}}{\left(x \right)} \operatorname{acos}{\left(x \right)}} + \frac{3 \sqrt{\cos{\left(x \right)}}}{2 \sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{\sqrt{\cos{\left(x \right)}}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{2 \sqrt{\cos{\left(x \right)}}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(x \right)}}\right) \operatorname{acos}^{\sqrt{\cos{\left(x \right)}}}{\left(x \right)}$$
Gráfico