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=arccos(3x)^(lg(5x- uno))
- y es igual a arc coseno de (3x) en el grado (lg(5x menos 1))
- y es igual a arc coseno de (3x) en el grado (lg(5x menos uno))
- y=arccos(3x)(lg(5x-1))
- y=arccos3xlg5x-1
- y=arccos3x^lg5x-1
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Expresiones semejantes
- y=arccos(3x)^(lg(5x+1))
Derivada de y=arccos(3x)^(lg(5x-1))
Solución
Ha introducido
[src]
log(5*x - 1) acos (3*x)
$$\operatorname{acos}^{\log{\left(5 x - 1 \right)}}{\left(3 x \right)}$$
acos(3*x)^log(5*x - 1)
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]
log(5*x - 1) /5*log(acos(3*x)) 3*log(5*x - 1) \
acos (3*x)*|---------------- - -----------------------|
| 5*x - 1 __________ |
| / 2 |
\ \/ 1 - 9*x *acos(3*x)/
$$\left(\frac{5 \log{\left(\operatorname{acos}{\left(3 x \right)} \right)}}{5 x - 1} - \frac{3 \log{\left(5 x - 1 \right)}}{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}}\right) \operatorname{acos}^{\log{\left(5 x - 1 \right)}}{\left(3 x \right)}$$
Segunda derivada
[src]
/ 2 \
log(-1 + 5*x) |/5*log(acos(3*x)) 3*log(-1 + 5*x) \ 25*log(acos(3*x)) 30 9*log(-1 + 5*x) 27*x*log(-1 + 5*x) |
acos (3*x)*||---------------- - -----------------------| - ----------------- - ---------------------------------- + ---------------------- - -----------------------|
|| -1 + 5*x __________ | 2 __________ / 2\ 2 3/2 |
|| / 2 | (-1 + 5*x) / 2 \-1 + 9*x /*acos (3*x) / 2\ |
\\ \/ 1 - 9*x *acos(3*x)/ \/ 1 - 9*x *(-1 + 5*x)*acos(3*x) \1 - 9*x / *acos(3*x)/
$$\left(- \frac{27 x \log{\left(5 x - 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(3 x \right)}} + \left(\frac{5 \log{\left(\operatorname{acos}{\left(3 x \right)} \right)}}{5 x - 1} - \frac{3 \log{\left(5 x - 1 \right)}}{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}}\right)^{2} + \frac{9 \log{\left(5 x - 1 \right)}}{\left(9 x^{2} - 1\right) \operatorname{acos}^{2}{\left(3 x \right)}} - \frac{25 \log{\left(\operatorname{acos}{\left(3 x \right)} \right)}}{\left(5 x - 1\right)^{2}} - \frac{30}{\sqrt{1 - 9 x^{2}} \left(5 x - 1\right) \operatorname{acos}{\left(3 x \right)}}\right) \operatorname{acos}^{\log{\left(5 x - 1 \right)}}{\left(3 x \right)}$$
Tercera derivada
[src]
/ 3 2 \
log(-1 + 5*x) |/5*log(acos(3*x)) 3*log(-1 + 5*x) \ /5*log(acos(3*x)) 3*log(-1 + 5*x) \ /25*log(acos(3*x)) 9*log(-1 + 5*x) 30 27*x*log(-1 + 5*x) \ 250*log(acos(3*x)) 54*log(-1 + 5*x) 27*log(-1 + 5*x) 135 225 729*x *log(-1 + 5*x) 405*x 243*x*log(-1 + 5*x) |
acos (3*x)*||---------------- - -----------------------| - 3*|---------------- - -----------------------|*|----------------- - ---------------------- + ---------------------------------- + -----------------------| + ------------------ - ------------------------ - ----------------------- + --------------------------------- + ----------------------------------- - ----------------------- - ---------------------------------- - -----------------------|
|| -1 + 5*x __________ | | -1 + 5*x __________ | | 2 / 2\ 2 __________ 3/2 | 3 3/2 3/2 / 2\ 2 __________ 5/2 3/2 2 |
|| / 2 | | / 2 | | (-1 + 5*x) \-1 + 9*x /*acos (3*x) / 2 / 2\ | (-1 + 5*x) / 2\ 3 / 2\ (-1 + 5*x)*\-1 + 9*x /*acos (3*x) / 2 2 / 2\ / 2\ / 2\ 2 |
\\ \/ 1 - 9*x *acos(3*x)/ \ \/ 1 - 9*x *acos(3*x)/ \ \/ 1 - 9*x *(-1 + 5*x)*acos(3*x) \1 - 9*x / *acos(3*x)/ \1 - 9*x / *acos (3*x) \1 - 9*x / *acos(3*x) \/ 1 - 9*x *(-1 + 5*x) *acos(3*x) \1 - 9*x / *acos(3*x) \1 - 9*x / *(-1 + 5*x)*acos(3*x) \-1 + 9*x / *acos (3*x)/
$$\left(- \frac{729 x^{2} \log{\left(5 x - 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}} \operatorname{acos}{\left(3 x \right)}} - \frac{243 x \log{\left(5 x - 1 \right)}}{\left(9 x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(3 x \right)}} - \frac{405 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \left(5 x - 1\right) \operatorname{acos}{\left(3 x \right)}} + \left(\frac{5 \log{\left(\operatorname{acos}{\left(3 x \right)} \right)}}{5 x - 1} - \frac{3 \log{\left(5 x - 1 \right)}}{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}}\right)^{3} - 3 \left(\frac{5 \log{\left(\operatorname{acos}{\left(3 x \right)} \right)}}{5 x - 1} - \frac{3 \log{\left(5 x - 1 \right)}}{\sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}}\right) \left(\frac{27 x \log{\left(5 x - 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(3 x \right)}} - \frac{9 \log{\left(5 x - 1 \right)}}{\left(9 x^{2} - 1\right) \operatorname{acos}^{2}{\left(3 x \right)}} + \frac{25 \log{\left(\operatorname{acos}{\left(3 x \right)} \right)}}{\left(5 x - 1\right)^{2}} + \frac{30}{\sqrt{1 - 9 x^{2}} \left(5 x - 1\right) \operatorname{acos}{\left(3 x \right)}}\right) + \frac{135}{\left(5 x - 1\right) \left(9 x^{2} - 1\right) \operatorname{acos}^{2}{\left(3 x \right)}} + \frac{250 \log{\left(\operatorname{acos}{\left(3 x \right)} \right)}}{\left(5 x - 1\right)^{3}} + \frac{225}{\sqrt{1 - 9 x^{2}} \left(5 x - 1\right)^{2} \operatorname{acos}{\left(3 x \right)}} - \frac{27 \log{\left(5 x - 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(3 x \right)}} - \frac{54 \log{\left(5 x - 1 \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(3 x \right)}}\right) \operatorname{acos}^{\log{\left(5 x - 1 \right)}}{\left(3 x \right)}$$
Gráfico