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
-
¿Cómo usar?
- Derivada de:
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Derivada de 1/t
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Derivada de f(x)=√x
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Expresiones idénticas
- y=((ch(x))^(tres / dos))/arctg5x
- y es igual a ((ch(x)) en el grado (3 dividir por 2)) dividir por arctg5x
- y es igual a ((ch(x)) en el grado (tres dividir por dos)) dividir por arctg5x
- y=((ch(x))(3/2))/arctg5x
- y=chx3/2/arctg5x
- y=chx^3/2/arctg5x
- y=((ch(x))^(3 dividir por 2)) dividir por arctg5x
Derivada de y=((ch(x))^(3/2))/arctg5x
Solución
Ha introducido
[src]
3/2 cosh (x) ---------- atan(5*x)
$$\frac{\cosh^{\frac{3}{2}}{\left(x \right)}}{\operatorname{atan}{\left(5 x \right)}}$$
cosh(x)^(3/2)/atan(5*x)
Primera derivada
[src]
3/2 _________
5*cosh (x) 3*\/ cosh(x) *sinh(x)
- ---------------------- + ---------------------
/ 2\ 2 2*atan(5*x)
\1 + 25*x /*atan (5*x)
$$\frac{3 \sinh{\left(x \right)} \sqrt{\cosh{\left(x \right)}}}{2 \operatorname{atan}{\left(5 x \right)}} - \frac{5 \cosh^{\frac{3}{2}}{\left(x \right)}}{\left(25 x^{2} + 1\right) \operatorname{atan}^{2}{\left(5 x \right)}}$$
Segunda derivada
[src]
3/2 / 1 \
3/2 2 _________ 50*cosh (x)*|--------- + 5*x|
3*cosh (x) 3*sinh (x) 15*\/ cosh(x) *sinh(x) \atan(5*x) /
------------ + ------------- - ---------------------- + -------------------------------
2 _________ / 2\ 2
4*\/ cosh(x) \1 + 25*x /*atan(5*x) / 2\
\1 + 25*x / *atan(5*x)
---------------------------------------------------------------------------------------
atan(5*x)
$$\frac{\frac{50 \left(5 x + \frac{1}{\operatorname{atan}{\left(5 x \right)}}\right) \cosh^{\frac{3}{2}}{\left(x \right)}}{\left(25 x^{2} + 1\right)^{2} \operatorname{atan}{\left(5 x \right)}} + \frac{3 \sinh^{2}{\left(x \right)}}{4 \sqrt{\cosh{\left(x \right)}}} + \frac{3 \cosh^{\frac{3}{2}}{\left(x \right)}}{2} - \frac{15 \sinh{\left(x \right)} \sqrt{\cosh{\left(x \right)}}}{\left(25 x^{2} + 1\right) \operatorname{atan}{\left(5 x \right)}}}{\operatorname{atan}{\left(5 x \right)}}$$
Tercera derivada
[src]
/ 2 \ / 2 \ / 2 \
| _________ sinh (x) | | 3/2 sinh (x) | 3/2 | 3 100*x 30*x |
3*|- 10*\/ cosh(x) + ----------|*sinh(x) 45*|2*cosh (x) + -----------| 250*cosh (x)*|-1 + ---------------------- + --------- + ---------------------| _________ / 1 \
| 3/2 | | _________| | / 2\ 2 2 / 2\ | 225*\/ cosh(x) *|--------- + 5*x|*sinh(x)
\ cosh (x)/ \ \/ cosh(x) / \ \1 + 25*x /*atan (5*x) 1 + 25*x \1 + 25*x /*atan(5*x)/ \atan(5*x) /
- ----------------------------------------- - ------------------------------- - -------------------------------------------------------------------------------- + -----------------------------------------
8 / 2\ 2 2
4*\1 + 25*x /*atan(5*x) / 2\ / 2\
\1 + 25*x / *atan(5*x) \1 + 25*x / *atan(5*x)
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
atan(5*x)
$$\frac{\frac{225 \left(5 x + \frac{1}{\operatorname{atan}{\left(5 x \right)}}\right) \sinh{\left(x \right)} \sqrt{\cosh{\left(x \right)}}}{\left(25 x^{2} + 1\right)^{2} \operatorname{atan}{\left(5 x \right)}} - \frac{3 \left(\frac{\sinh^{2}{\left(x \right)}}{\cosh^{\frac{3}{2}}{\left(x \right)}} - 10 \sqrt{\cosh{\left(x \right)}}\right) \sinh{\left(x \right)}}{8} - \frac{45 \left(\frac{\sinh^{2}{\left(x \right)}}{\sqrt{\cosh{\left(x \right)}}} + 2 \cosh^{\frac{3}{2}}{\left(x \right)}\right)}{4 \left(25 x^{2} + 1\right) \operatorname{atan}{\left(5 x \right)}} - \frac{250 \left(\frac{100 x^{2}}{25 x^{2} + 1} + \frac{30 x}{\left(25 x^{2} + 1\right) \operatorname{atan}{\left(5 x \right)}} - 1 + \frac{3}{\left(25 x^{2} + 1\right) \operatorname{atan}^{2}{\left(5 x \right)}}\right) \cosh^{\frac{3}{2}}{\left(x \right)}}{\left(25 x^{2} + 1\right)^{2} \operatorname{atan}{\left(5 x \right)}}}{\operatorname{atan}{\left(5 x \right)}}$$
Gráfico