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 1/(x+3)
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Derivada de 4*y
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Derivada de (-1)/x-3*x
- Derivada de y=ax
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Expresiones idénticas
- y=arctg(cos5x)/cos5x
- y es igual a arctg( coseno de 5x) dividir por coseno de 5x
- y=arctgcos5x/cos5x
- y=arctg(cos5x) dividir por cos5x
Derivada de y=arctg(cos5x)/cos5x
Solución
Ha introducido
[src]
atan(cos(5*x)) -------------- cos(5*x)
$$\frac{\operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{\cos{\left(5 x \right)}}$$
atan(cos(5*x))/cos(5*x)
Primera derivada
[src]
5*sin(5*x) 5*atan(cos(5*x))*sin(5*x) - ------------------------ + ------------------------- / 2 \ 2 \1 + cos (5*x)/*cos(5*x) cos (5*x)
$$\frac{5 \sin{\left(5 x \right)} \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{\cos^{2}{\left(5 x \right)}} - \frac{5 \sin{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right) \cos{\left(5 x \right)}}$$
Segunda derivada
[src]
/ 2 / 2 \ \ | 2*sin (5*x) | 2*sin (5*x)| | | 1 + ------------- |1 + -----------|*atan(cos(5*x)) | | 2 | 2 | 2 | | 1 + cos (5*x) \ cos (5*x) / 2*sin (5*x) | 25*|- ----------------- + -------------------------------- - -------------------------| | 2 cos(5*x) / 2 \ 2 | \ 1 + cos (5*x) \1 + cos (5*x)/*cos (5*x)/
$$25 \left(- \frac{1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1}}{\cos^{2}{\left(5 x \right)} + 1} + \frac{\left(\frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 1\right) \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{\cos{\left(5 x \right)}} - \frac{2 \sin^{2}{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right) \cos^{2}{\left(5 x \right)}}\right)$$
Tercera derivada
[src]
/ 2 2 2 2 \
| 6*cos (5*x) 2*sin (5*x) 8*cos (5*x)*sin (5*x) / 2 \ / 2 \ / 2 \ |
|1 - ------------- + ------------- - --------------------- | 2*sin (5*x) | | 2*sin (5*x)| | 6*sin (5*x)| |
| 2 2 2 3*|1 + -------------| 3*|1 + -----------| |5 + -----------|*atan(cos(5*x))|
| 1 + cos (5*x) 1 + cos (5*x) / 2 \ | 2 | | 2 | | 2 | |
| \1 + cos (5*x)/ \ 1 + cos (5*x)/ \ cos (5*x) / \ cos (5*x) / |
125*|--------------------------------------------------------- - --------------------- - ------------------- + --------------------------------|*sin(5*x)
| 2 2 2 cos(5*x) |
\ 1 + cos (5*x) 1 + cos (5*x) 1 + cos (5*x) /
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cos(5*x)
$$\frac{125 \left(- \frac{3 \left(1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1}\right)}{\cos^{2}{\left(5 x \right)} + 1} - \frac{3 \left(\frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 1\right)}{\cos^{2}{\left(5 x \right)} + 1} + \frac{\left(\frac{6 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)}} + 5\right) \operatorname{atan}{\left(\cos{\left(5 x \right)} \right)}}{\cos{\left(5 x \right)}} + \frac{1 + \frac{2 \sin^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1} - \frac{6 \cos^{2}{\left(5 x \right)}}{\cos^{2}{\left(5 x \right)} + 1} - \frac{8 \sin^{2}{\left(5 x \right)} \cos^{2}{\left(5 x \right)}}{\left(\cos^{2}{\left(5 x \right)} + 1\right)^{2}}}{\cos^{2}{\left(5 x \right)} + 1}\right) \sin{\left(5 x \right)}}{\cos{\left(5 x \right)}}$$
Gráfico