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^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de y=-6/x
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Expresiones idénticas
- y=arccos4x^ tres /sh^4x
- y es igual a arc coseno de 4x al cubo dividir por sh en el grado 4x
- y es igual a arc coseno de 4x en el grado tres dividir por sh en el grado 4x
- y=arccos4x3/sh4x
- y=arccos4x³/sh⁴x
- y=arccos4x en el grado 3/sh en el grado 4x
- y=arccos4x^3 dividir por sh^4x
Derivada de y=arccos4x^3/sh^4x
Solución
Ha introducido
[src]
3
acos (4*x)
----------
4
sinh (x)
$$\frac{\operatorname{acos}^{3}{\left(4 x \right)}}{\sinh^{4}{\left(x \right)}}$$
acos(4*x)^3/sinh(x)^4
Primera derivada
[src]
2 3
12*acos (4*x) 4*acos (4*x)*cosh(x)
- ----------------------- - --------------------
___________ 5
/ 2 4 sinh (x)
\/ 1 - 16*x *sinh (x)
$$- \frac{4 \cosh{\left(x \right)} \operatorname{acos}^{3}{\left(4 x \right)}}{\sinh^{5}{\left(x \right)}} - \frac{12 \operatorname{acos}^{2}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \sinh^{4}{\left(x \right)}}$$
Segunda derivada
[src]
/ / 2 \ \
| 24 2 | 5*cosh (x)| 48*x*acos(4*x) 24*acos(4*x)*cosh(x) |
4*|- ---------- - acos (4*x)*|1 - ----------| - -------------- + ----------------------|*acos(4*x)
| 2 | 2 | 3/2 ___________ |
| -1 + 16*x \ sinh (x) / / 2\ / 2 |
\ \1 - 16*x / \/ 1 - 16*x *sinh(x)/
--------------------------------------------------------------------------------------------------
4
sinh (x)
$$\frac{4 \left(- \frac{48 x \operatorname{acos}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \left(1 - \frac{5 \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) \operatorname{acos}^{2}{\left(4 x \right)} - \frac{24}{16 x^{2} - 1} + \frac{24 \cosh{\left(x \right)} \operatorname{acos}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}} \sinh{\left(x \right)}}\right) \operatorname{acos}{\left(4 x \right)}}{\sinh^{4}{\left(x \right)}}$$
Tercera derivada
[src]
/ / 2 \ / 2 \ / 1 2*x*acos(4*x) \ \
| 2 | 5*cosh (x)| 3 | 15*cosh (x)| 144*|---------- + --------------|*acos(4*x)*cosh(x)|
| 18*acos (4*x)*|1 - ----------| acos (4*x)*|7 - -----------|*cosh(x) | 2 3/2| |
| 2 2 2 | 2 | | 2 | |-1 + 16*x / 2\ | |
| 48 24*acos (4*x) 1152*x *acos (4*x) \ sinh (x) / 576*x*acos(4*x) \ sinh (x) / \ \1 - 16*x / / |
8*|- -------------- - -------------- - ------------------ + ------------------------------ + --------------- + ------------------------------------ + ---------------------------------------------------|
| 3/2 3/2 5/2 ___________ 2 sinh(x) sinh(x) |
| / 2\ / 2\ / 2\ / 2 / 2\ |
\ \1 - 16*x / \1 - 16*x / \1 - 16*x / \/ 1 - 16*x \-1 + 16*x / /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
4
sinh (x)
$$\frac{8 \left(- \frac{1152 x^{2} \operatorname{acos}^{2}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{5}{2}}} + \frac{576 x \operatorname{acos}{\left(4 x \right)}}{\left(16 x^{2} - 1\right)^{2}} + \frac{\left(7 - \frac{15 \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) \cosh{\left(x \right)} \operatorname{acos}^{3}{\left(4 x \right)}}{\sinh{\left(x \right)}} + \frac{144 \left(\frac{2 x \operatorname{acos}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{16 x^{2} - 1}\right) \cosh{\left(x \right)} \operatorname{acos}{\left(4 x \right)}}{\sinh{\left(x \right)}} + \frac{18 \left(1 - \frac{5 \cosh^{2}{\left(x \right)}}{\sinh^{2}{\left(x \right)}}\right) \operatorname{acos}^{2}{\left(4 x \right)}}{\sqrt{1 - 16 x^{2}}} - \frac{24 \operatorname{acos}^{2}{\left(4 x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{48}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}}\right)}{\sinh^{4}{\left(x \right)}}$$
Gráfico